DATS 6101 - Midterm
Name: Snehitha Tadapaneni, Sai Rachana Kandikattu, Amrutha Jayachandradhara, Wilona Nguyen, Pramod Krishnachari
2024-10-26
Introduction
Our research focuses on performing Exploratory Data Analysis (EDA) on Google Play Store apps to uncover patterns, trends, and insights regarding app characteristics, user behavior, and installation patterns. We are trying to see how app popularity, defined as the number of installs with high reviews and ratings, is impacted by categories, last updated, app sizes, version, and other factors.
Smart Question
“What is the impact of content rating, required Android version, app category, size, and pricing on predicting app success in terms of positive ratings and high user reviews, as well as the number of installs, using data from Google Play Store apps from 2010 to 2018?”
Specific: The question clearly defines the variables (content rating, required Android version, app category, size, pricing) and the outcomes (positive ratings, high user reviews, number of installs).
Measurable: The outcomes (positive ratings, high user reviews, number of installs) are quantifiable.
Achievable: Given the availability of Google Play Store data from 2010 to 2018, the analysis is feasible.
Relevant: The question addresses a significant issue in the app development and marketing industry: predicting app success.
Time-specific: The timeframe (2010-2018) is clearly defined.
Data Preparation and Cleaning
Here, we have loaded the dataset ‘Google Play Store Apps’ stored in a CSV file using the read.csv function, which reads the CSV file into a data frame, and then we assigned it to the variable data_apps.
#Loading the Dataset
data_apps <- data.frame(read.csv("googleplaystore.csv"))#Checking the structure of the data
str(data_apps)## 'data.frame': 10841 obs. of 13 variables:
## $ App : chr "Photo Editor & Candy Camera & Grid & ScrapBook" "Coloring book moana" "U Launcher Lite – FREE Live Cool Themes, Hide Apps" "Sketch - Draw & Paint" ...
## $ Category : chr "ART_AND_DESIGN" "ART_AND_DESIGN" "ART_AND_DESIGN" "ART_AND_DESIGN" ...
## $ Rating : num 4.1 3.9 4.7 4.5 4.3 4.4 3.8 4.1 4.4 4.7 ...
## $ Reviews : chr "159" "967" "87510" "215644" ...
## $ Size : chr "19M" "14M" "8.7M" "25M" ...
## $ Installs : chr "10,000+" "500,000+" "5,000,000+" "50,000,000+" ...
## $ Type : chr "Free" "Free" "Free" "Free" ...
## $ Price : chr "0" "0" "0" "0" ...
## $ Content.Rating: chr "Everyone" "Everyone" "Everyone" "Teen" ...
## $ Genres : chr "Art & Design" "Art & Design;Pretend Play" "Art & Design" "Art & Design" ...
## $ Last.Updated : chr "January 7, 2018" "January 15, 2018" "August 1, 2018" "June 8, 2018" ...
## $ Current.Ver : chr "1.0.0" "2.0.0" "1.2.4" "Varies with device" ...
## $ Android.Ver : chr "4.0.3 and up" "4.0.3 and up" "4.0.3 and up" "4.2 and up" ...#First 5 rows of the dataset
head(data_apps)## App Category Rating
## 1 Photo Editor & Candy Camera & Grid & ScrapBook ART_AND_DESIGN 4.1
## 2 Coloring book moana ART_AND_DESIGN 3.9
## 3 U Launcher Lite – FREE Live Cool Themes, Hide Apps ART_AND_DESIGN 4.7
## 4 Sketch - Draw & Paint ART_AND_DESIGN 4.5
## 5 Pixel Draw - Number Art Coloring Book ART_AND_DESIGN 4.3
## 6 Paper flowers instructions ART_AND_DESIGN 4.4
## Reviews Size Installs Type Price Content.Rating Genres
## 1 159 19M 10,000+ Free 0 Everyone Art & Design
## 2 967 14M 500,000+ Free 0 Everyone Art & Design;Pretend Play
## 3 87510 8.7M 5,000,000+ Free 0 Everyone Art & Design
## 4 215644 25M 50,000,000+ Free 0 Teen Art & Design
## 5 967 2.8M 100,000+ Free 0 Everyone Art & Design;Creativity
## 6 167 5.6M 50,000+ Free 0 Everyone Art & Design
## Last.Updated Current.Ver Android.Ver
## 1 January 7, 2018 1.0.0 4.0.3 and up
## 2 January 15, 2018 2.0.0 4.0.3 and up
## 3 August 1, 2018 1.2.4 4.0.3 and up
## 4 June 8, 2018 Varies with device 4.2 and up
## 5 June 20, 2018 1.1 4.4 and up
## 6 March 26, 2017 1.0 2.3 and upDescription of the App Dataset Columns
- App: The name of the application, represented as a character string.
- Category: The main category of the app, such as “ART_AND_DESIGN,” represented as a character string.
- Rating: The average user rating of the app, recorded as a numeric value.
- Reviews: The total number of user reviews for the app, shown as a character string.
- Size: The size of the application, represented as a character string.
- Installs: The approximate number of installations for the app, stored as a character string.
- Type: Indicates whether the app is free or paid, represented as a character string.
- Price: The price of the app, stored as a character string. Free apps are listed as “0,” while paid apps have a dollar amount.
- Content.Rating: The target age group for the app, represented as a character string.
- Genres: The genre(s) of the app.
- Last.Updated: The date of the app’s last update, stored as a character string.
- Current.Ver: The current version of the app, represented as a character string.
- Android.Ver: The minimum Android version required to run the app, stored as a character string.
Apps
# Checking the type of the App
typeof(data_apps$App)## [1] "character"Checking for duplicated apps and removing
#Display all the duplicated Apps
duplicate_apps <- aggregate(App ~ ., data = data_apps, FUN = length)
duplicate_apps <- duplicate_apps[duplicate_apps$App > 1, ]
duplicate_apps <- duplicate_apps[order(-duplicate_apps$App), ]
#View(duplicate_apps)
#print(duplicate_apps)
print(paste("Number of duplicated Apps:",nrow(duplicate_apps)))## [1] "Number of duplicated Apps: 404"#Removing Na values and duplicates
data_clean <- data_apps[!is.na(data_apps$App), ]
data_clean <- data_clean[!duplicated(data_clean$App), ]
#(After removing the duplicates) Unique values
unique_apps <- length(unique(data_clean$App))
print(paste("Number of unique apps after removing the duplicates:", unique_apps))## [1] "Number of unique apps after removing the duplicates: 9660"Duplicate App Analysis:
- 404 apps were repeated either twice or thrice.
- After removing duplicates, the dataset now contains 9660 unique apps.
- Total duplicates removed: 1181 apps.
After dropping duplicate
str(data_clean$App)## chr [1:9660] "Photo Editor & Candy Camera & Grid & ScrapBook" ...Price
typeof(data_apps$Price)## [1] "character"Convertion of Price to numerical
There is ‘$’ present after each price of the App. Check and remove before conversion.
#To check if there is dollar symbol present
#data_clean$Price[]# Remove dollar symbols and convert to numeric
data_clean$Price <- as.numeric(gsub("\\$", "", data_clean$Price))#Recheck for dollar symbol
#data_clean$Price[]All the dollar symbols are removed succesfully.
# Summary statistics for price
summary(data_clean$Price)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.000 0.000 0.000 1.099 0.000 400.000 1From the unique_df, there is a missing value present in the Price column. Let’s handle it!
Checking for missing values in Price
missing_na <- is.na(data_clean$Price)
missing_blank <- data_clean$Price == ""
sum(missing_na)## [1] 1sum(missing_blank, na.rm = TRUE)## [1] 0# Remove row where Price is NA or blank
data_clean <- data_clean[!is.na(data_clean$Price) & data_clean$Price != "", ]Have removed one row #10473 which app does not have a category nameas it is not relevant to our analysis.
#Recheck for missing values
summary(data_clean$Price)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 0.000 1.099 0.000 400.000Missing values removed succesfully. (Price)
Type
#Checking the type of Type variable
table(data_clean$Type)##
## Free Paid
## 8902 756From the price column, we can see 8903 apps are free but it is misread somewhere in the Type column. So lets check!
#Checking for Missing values
print(paste("Missing values:",sum(is.na(data_clean$Type))))## [1] "Missing values: 0"data_clean[is.na(data_clean$Type), ]## [1] App Category Rating Reviews Size
## [6] Installs Type Price Content.Rating Genres
## [11] Last.Updated Current.Ver Android.Ver
## <0 rows> (or 0-length row.names)# Replace NaN or missing values in the Type column with "Free"
data_clean$Type[is.na(data_clean$Type)] <- "Free"There is one row 9150, has a missing value for Type. As the price is 0, replaced it with “Free”.
Missing values handles succesfully. (Type)
Size
# Checking the type of the Size
typeof(data_apps$Size)## [1] "character"Replacing Misiing values with the mean (Size)
# Replace "Varies with Device" in the Size column with NA
data_clean$Size[data_clean$Size == "Varies with device"] <- NA
data_clean <- data_clean[!grepl("\\+", data_clean$Size), ]
data_clean$Size <- ifelse(grepl("k", data_clean$Size),
as.numeric(gsub("k", "", data_clean$Size)) *
0.001, # Convert "K" to MB
as.numeric(gsub("M", "", data_clean$Size)))
# Remove "M" for megabytes
# Calculate and display the mean size for each category in the 'Type' column
mean_size_by_type <- tapply(data_clean$Size, data_clean$Category,
mean, na.rm = TRUE)
print(mean_size_by_type)## ART_AND_DESIGN AUTO_AND_VEHICLES BEAUTY BOOKS_AND_REFERENCE
## 12.370968 20.037147 13.795745 13.134701
## BUSINESS COMICS COMMUNICATION DATING
## 13.867194 13.794959 11.307430 15.661119
## EDUCATION ENTERTAINMENT EVENTS FAMILY
## 19.057101 23.043750 13.963754 27.187988
## FINANCE FOOD_AND_DRINK GAME HEALTH_AND_FITNESS
## 17.368127 20.494318 41.866609 20.669707
## HOUSE_AND_HOME LIBRARIES_AND_DEMO LIFESTYLE MAPS_AND_NAVIGATION
## 15.970258 10.602883 14.844916 16.368121
## MEDICAL NEWS_AND_MAGAZINES PARENTING PERSONALIZATION
## 19.189399 12.470189 22.512963 11.224624
## PHOTOGRAPHY PRODUCTIVITY SHOPPING SOCIAL
## 15.666158 12.342505 15.491435 15.984090
## SPORTS TOOLS TRAVEL_AND_LOCAL VIDEO_PLAYERS
## 24.058361 8.782837 24.204410 15.792756
## WEATHER
## 12.680036# Loop through each row and replace NA values in the Size column with the mean size of the corresponding category
data_clean$Size <- ifelse(
is.na(data_clean$Size), # Check if Size is NA
round(mean_size_by_type[data_clean$Category], 1), # Replace with the mean size based on the Category
data_clean$Size # Keep the original size if it's not NA
)Installs
Remove the ‘+’ sign, Remove the commas, Convert to numeric
#clean installations
clean_installs <- function(Installs) {
Installs <- gsub("\\+", "", Installs)
Installs <- gsub(",", "", Installs)
return(as.numeric(Installs))
}
data_clean$Installs <- sapply(data_clean$Installs, clean_installs)
nan_rows <- sapply(data_clean[, c("Size", "Installs")], function(x) any(is.nan(x)))
# Display only rows that contain NaN in either Size or Installs
data_clean[,nan_rows]## data frame with 0 columns and 9659 rowsdatatable((data_clean), options = list(scrollX = TRUE ))Display the unique values
data_clean <- data_clean %>%
mutate(Rating = ifelse(is.na(Rating), mean(Rating, na.rm = TRUE), Rating))
# Identify the unique values in the 'Installs' column
unique_values <- unique(data_clean$Installs)
# Display the unique values
print(unique_values)## [1] 1e+04 5e+05 5e+06 5e+07 1e+05 5e+04 1e+06 1e+07 5e+03 1e+08 1e+09 1e+03
## [13] 5e+08 5e+01 1e+02 5e+02 1e+01 1e+00 5e+00 0e+00# Function to convert the installs to numeric
convert_to_numeric <- function(x) {
# Remove non-numeric characters and convert to numeric
as.numeric(gsub("[^0-9]", "", x)) * 10^(length(gregexpr(",", x)[[1]]) - 1)
}
# Sort unique values based on the custom numeric conversion
sorted_values <- unique_values[order(sapply(unique_values, convert_to_numeric))]Rating and Reviews
# Checking the type of the Rating
typeof(data_clean$Rating)## [1] "double"# Checking the type of the Reviews
typeof(data_clean$Reviews)## [1] "character"Checking the format of Rating and Reviews
## chr [1:9659] "159" "967" "87510" "215644" "967" "167" "178" "36815" ...## num [1:9659] 4.1 3.9 4.7 4.5 4.3 4.4 3.8 4.1 4.4 4.7 ...As we can see the Review column is in string format which could be converted into int for more insights.
Checking the unique values for reviews and rating
unique_values <- unique(data_clean$Reviews)
unique_values1 <- unique(data_clean$Rating)
# Display the unique values
print(unique_values)## [1] "159" "967" "87510" "215644" "167" "178"
## [7] "36815" "13791" "121" "13880" "8788" "44829"
## [13] "4326" "1518" "55" "3632" "27" "194216"
## [19] "224399" "450" "654" "7699" "61" "118"
## [25] "192" "20260" "203" "136" "223" "1120"
## [31] "227" "5035" "1015" "353" "564" "8145"
## [37] "36639" "158" "591" "117" "176" "295221"
## [43] "2206" "26" "174531" "1070" "85" "845"
## [49] "367" "1598" "284" "17057" "129" "542"
## [55] "10479" "805" "1403" "3971" "534" "7774"
## [61] "38846" "2431" "6090" "295" "190" "40211"
## [67] "356" "52530" "116986" "1379" "271920" "736"
## [73] "7021" "197" "737" "3574" "994" "197136"
## [79] "142" "15168" "2155" "138" "5414" "21777"
## [85] "348" "250" "13372" "7880" "3617" "4806"
## [91] "65786" "31433" "5097" "1754" "2680" "1288"
## [97] "18900" "49790" "1150" "1739" "32090" "2225"
## [103] "4369" "8572" "964" "42050" "104" "17934"
## [109] "601" "36" "187" "182" "30" "134"
## [115] "74" "113715" "3595" "9315" "75" "38"
## [121] "26834" "119" "2277" "2280" "184" "9"
## [127] "77" "35" "364" "18" "473" "66"
## [133] "3871" "257" "62" "2914724" "1857" "4478"
## [139] "577550" "814080" "246315" "454060" "155446" "418"
## [145] "22486" "203130" "1435" "116507" "1433233" "90468"
## [151] "860" "363934" "87873" "17506" "1862" "2084"
## [157] "47303" "19080" "161" "85842" "7831" "91615"
## [163] "4620" "21336" "26875" "1778" "2709" "64513"
## [169] "8342" "527" "1322" "1680" "2739" "1065"
## [175] "233757" "2" "51269" "30105" "156" "114"
## [181] "341157" "16129" "674730" "1254730" "85185" "32584"
## [187] "217730" "70991" "1002861" "16589" "148945" "4458"
## [193] "62272" "8941" "46353" "1279184" "88073" "67000"
## [199] "159872" "30847" "188841" "11622" "95912" "4034"
## [205] "45964" "14955" "6903" "31614" "23055" "19023"
## [211] "207372" "1225" "380837" "10600" "74359" "822"
## [217] "80805" "2287" "4162" "14760" "23243" "8978"
## [223] "42492" "286897" "103755" "46505" "11442" "10295"
## [229] "296" "29313" "51507" "1802" "1383" "23175"
## [235] "5868" "2111" "5448" "4159" "20815" "78662"
## [241] "7149" "3079" "5800" "6989" "16422" "108741"
## [247] "624" "1661" "97702" "308" "5211" "1058"
## [253] "78172" "413" "1013635" "24005" "57106" "2249"
## [259] "516" "834" "1010" "238970" "302" "438"
## [265] "73" "39" "144" "2181" "93965" "1446"
## [271] "12088" "314" "25671" "15194" "22551" "29839"
## [277] "279" "564387" "1330" "1677" "757" "115"
## [283] "125" "9952" "18814" "21" "15" "51981"
## [289] "3596" "1006" "5968" "4895" "56642847" "69119316"
## [295] "125257" "9642995" "1429035" "4604324" "3419249" "11334799"
## [301] "158679" "3075028" "4187998" "659395" "4785892" "66602"
## [307] "30209" "36901" "5149854" "192948" "99559" "437674"
## [313] "13698" "2473509" "20769" "36880" "171031" "63543"
## [319] "45487" "615381" "2451083" "33053" "5387333" "3648120"
## [325] "136662" "42370" "781810" "3128250" "2083237" "541389"
## [331] "46702" "2939" "13761" "258556" "40751" "17712922"
## [337] "25021" "27187" "122498" "132014" "83239" "594728"
## [343] "10484169" "2876500" "28238" "335646" "350154" "349384"
## [349] "346982" "244863" "10790289" "330761" "37320" "12842860"
## [355] "2546527" "15880" "2264916" "42925" "2511130" "13100"
## [361] "27156" "55098" "1133501" "12578" "10965" "18247"
## [367] "190613" "125232" "72065" "27540" "104990" "177703"
## [373] "177263" "237468" "32254" "483565" "552441" "60308"
## [379] "457283" "93825" "32283" "15287" "205739" "14873"
## [385] "7820209" "9498" "88427" "305218" "183374" "20901"
## [391] "122595" "124346" "837842" "255" "41420" "44706"
## [397] "23707" "29208" "191032" "1545" "57" "0"
## [403] "4" "516801" "285726" "76646" "2556" "7779"
## [409] "61637" "12632" "313724" "48845" "305708" "31320"
## [415] "172460" "4195" "11633" "10212" "37053" "667"
## [421] "13202" "28671" "1157" "212626" "222888" "2067"
## [427] "1643" "105" "3414" "42194" "11806" "1999"
## [433] "22544" "97684" "2519" "1146" "13046" "17268"
## [439] "8722" "953" "2593" "5377" "852" "212"
## [445] "1972" "35206" "5164" "1939" "277" "80"
## [451] "825" "40035" "1093" "135418" "1601" "2212"
## [457] "57081" "241" "63986" "7888" "535" "5084"
## [463] "2430" "837" "738" "4631" "4953" "1439"
## [469] "337" "51698" "923" "149" "198" "23170"
## [475] "13890" "13440" "143" "1059" "894" "6191"
## [481] "15081" "218" "243950" "236" "5152" "1576"
## [487] "6701" "742" "2506" "182986" "8661" "8"
## [493] "59" "28" "185" "6" "110" "3"
## [499] "5" "84" "20" "776" "1" "14"
## [505] "24" "23" "11" "101" "120" "41605"
## [511] "791" "5323" "478" "69" "53" "6289924"
## [517] "181893" "2544" "85375" "314299" "9770" "32346"
## [523] "4075" "10611" "9321" "56065" "14286" "133136"
## [529] "2469" "36212" "390" "1090" "266948" "342918"
## [535] "748" "172640" "1619" "3168" "29855" "6736"
## [541] "7005" "889" "5741" "27572" "10852" "9888"
## [547] "1929" "1516" "215301" "423" "254519" "1107903"
## [553] "211856" "99020" "90481" "32381" "248912" "248555"
## [559] "272145" "56897" "8599" "41185" "29980" "304"
## [565] "358" "11904" "22251" "22384" "73404" "12733"
## [571] "25183" "52743" "61749" "55704" "19277" "13612"
## [577] "37862" "18372" "656" "240" "275" "3692"
## [583] "2363" "1769" "430" "756" "3963" "316"
## [589] "642" "172505" "69493" "7973" "5695" "142632"
## [595] "55256" "54798" "4815" "75112" "33646" "206527"
## [601] "9348" "3816" "47847" "16195" "206" "28392"
## [607] "3241" "835" "2525" "828" "200058" "1239"
## [613] "702" "108613" "148550" "3847" "84309" "14206"
## [619] "14700" "42828" "40209" "1405" "256079" "2078"
## [625] "16103" "31085" "3528" "5456208" "11656" "28948"
## [631] "296771" "470089" "10939" "98509" "5241" "22508"
## [637] "10291" "7165362" "4885646" "141980" "6979" "46618"
## [643] "103078" "17682" "37000" "175528" "1828284" "34923"
## [649] "684116" "46916" "407698" "702975" "32458" "235496"
## [655] "11661" "653008" "23063" "87384" "411683" "8918"
## [661] "501498" "2133296" "29690" "130549" "613059" "1633682"
## [667] "2646" "21867" "32732" "243747" "2639" "1511"
## [673] "44550" "7813" "1033" "2442" "15254" "155234"
## [679] "310066" "12216" "388089" "92058" "88185" "493"
## [685] "33387" "123279" "27424" "60841" "29706" "288150"
## [691] "14807" "319692" "61201" "22998" "12398" "35928"
## [697] "64448" "22378" "16372" "58028" "736864" "1968"
## [703] "35279" "17247" "87723" "18523" "182103" "197774"
## [709] "8674" "58082" "115033" "801" "8968" "303"
## [715] "732" "1856" "50725" "1575" "6238" "9941"
## [721] "23666" "67554" "38769" "160164" "3771" "256664"
## [727] "787177" "3782" "40113" "7074" "2153" "26089"
## [733] "20611" "811" "15558" "573" "37" "8232"
## [739] "3089" "3874" "464" "731" "8800" "99"
## [745] "456" "3200" "5839" "663" "16" "13"
## [751] "46" "1953" "12" "4298" "49" "100"
## [757] "399" "7" "124424" "39041" "52306" "36718"
## [763] "42644" "278082" "6076" "112656" "335738" "31906"
## [769] "20672" "957973" "130582" "31218" "167168" "34428"
## [775] "15247" "48445" "35518" "12185" "36746" "21996"
## [781] "138371" "12073" "111632" "250706" "706301" "64959"
## [787] "659741" "510392" "7215" "25508" "60449" "381788"
## [793] "10697" "347838" "31804" "3856" "199684" "44545"
## [799] "1336246" "57493" "283" "12304" "8188" "11919"
## [805] "45957" "126431" "21570" "134564" "16961" "111254"
## [811] "7731" "5928" "15703" "6148" "861" "8662"
## [817] "23130" "69973" "1311" "26587" "2417" "1054"
## [823] "25166" "129304" "19870" "161440" "7514" "46106"
## [829] "15141" "714" "42410" "260547" "4344" "22808"
## [835] "42809" "16808" "157505" "24647" "1922" "3334"
## [841] "10658" "78361" "2594" "13868" "135952" "11066"
## [847] "34861" "37580" "281485" "685" "3780" "15192"
## [853] "5950" "15993" "5905" "14627" "1098" "2898"
## [859] "70782" "11264" "100997" "3290" "341090" "87951"
## [865] "24729" "78306" "43313" "1374549" "208463" "6998"
## [871] "145323" "95" "64784" "32997" "82" "2707"
## [877] "129737" "611136" "6118" "2473" "109784" "3320"
## [883] "68103" "8412" "10741" "3803" "155944" "10159"
## [889] "28008" "43614" "455377" "1398" "1032935" "32405"
## [895] "151080" "22513" "90042" "58316" "8509" "19314"
## [901] "21314" "30224" "454" "14952" "1250" "1726"
## [907] "14065" "556" "4925" "6507" "11707" "1077"
## [913] "46539" "9066" "1962" "22071" "196" "278"
## [919] "61881" "2129" "1268" "91359" "22015" "131569"
## [925] "31986" "22875" "17071" "90242" "483960" "511228"
## [931] "1920" "40116" "51517" "7690" "321134" "3755"
## [937] "104504" "333208" "35218" "116403" "37517" "292969"
## [943] "428156" "1577" "38098" "31139" "272337" "220125"
## [949] "400592" "20098" "117925" "548021" "48276" "471036"
## [955] "12705" "706" "465" "644" "144040" "51227"
## [961] "357417" "199" "827597" "9116" "2071" "50294"
## [967] "708674" "1140" "232153" "14709" "12029" "1873516"
## [973] "2880" "270267" "559186" "77777" "8642" "501144"
## [979] "1861" "1203" "299" "115721" "14810" "183662"
## [985] "27393" "10445" "49479" "4848" "20812" "328469"
## [991] "100406" "205299" "66791" "399009" "5420" "130104"
## [997] "251534" "28951" "60096" "106547" "134195" "249855"
## [1003] "109756" "38343" "190247" "75571" "70769" "2107"
## [1009] "26540" "1608" "19074" "7976" "7586" "2885"
## [1015] "48226" "1026" "28945" "11506" "6826" "111450"
## [1021] "19543" "233243" "11689" "77563" "5499" "48286"
## [1027] "26652" "71269" "20301" "93691" "56145" "20326"
## [1033] "12955" "2681" "325738" "4102" "40296" "4559407"
## [1039] "570242" "121838" "62616" "12858" "34356" "50679"
## [1045] "16943" "524299" "267" "623" "117176" "70416"
## [1051] "15674" "14402" "141163" "69395" "27439" "2490"
## [1057] "24094" "18539" "3061" "229210" "20547" "3405"
## [1063] "217" "7895" "32606" "1324" "126017" "14394"
## [1069] "1812" "13724" "10253" "4642" "16570" "20161"
## [1075] "2894" "5038" "31665" "13799" "111462" "57634"
## [1081] "8576" "417907" "3167" "27386" "162243" "65913"
## [1087] "24977" "6000" "37711" "175293" "174" "353799"
## [1093] "2758" "1437" "7573" "8481" "10054" "10117"
## [1099] "39189" "3522" "71419" "36857" "39123" "14653"
## [1105] "23013" "287" "4435" "43800" "4281" "7508"
## [1111] "491" "160" "22584" "4087" "2496" "103305"
## [1117] "2669" "10" "7619" "126" "273" "2248"
## [1123] "809" "3280" "1478" "2382" "4450" "515"
## [1129] "4465" "2427" "6631" "11200" "6896" "3834"
## [1135] "81" "2087" "58" "3014" "487" "67007"
## [1141] "539" "126862" "48" "1465" "929" "783"
## [1147] "2907" "434" "54" "411" "237" "2580"
## [1153] "363" "130272" "91" "130" "25" "7396"
## [1159] "58055" "1703" "7750" "12657" "1919" "60170"
## [1165] "831" "8671" "31" "20145" "912" "102"
## [1171] "3945" "2221" "3781" "1267" "18968" "47497"
## [1177] "140995" "51357" "13565" "39364" "7287" "161143"
## [1183] "16168" "116079" "815893" "985" "4260" "726074"
## [1189] "3829" "33572" "6145" "34327" "7457" "41941"
## [1195] "82145" "10944" "665" "2167" "53652" "18961"
## [1201] "9412" "9663" "23164" "3031" "95557" "7869"
## [1207] "4212" "17368" "6554" "33264" "34782" "6676"
## [1213] "1067" "1797" "367505" "20304" "7376" "49147"
## [1219] "69177" "3448" "39724" "3788" "95736" "1658"
## [1225] "3309" "987" "5208" "78298" "6808" "12452"
## [1231] "360" "16637" "95904" "3114" "220" "33"
## [1237] "1533" "28301" "3937" "21195" "2042" "13213"
## [1243] "118034" "9464" "10097" "28588" "19621" "10544"
## [1249] "4427" "50338" "3346" "4447388" "27722264" "22426677"
## [1255] "254258" "148897" "369203" "5234162" "23133508" "8118609"
## [1261] "10485308" "1497361" "59800" "2610526" "4066989" "3778921"
## [1267] "6198563" "10306" "44891723" "1000417" "17039" "685981"
## [1273] "10393" "14198297" "592068" "1732263" "295241" "1135631"
## [1279] "5566669" "1295557" "270687" "2157930" "506275" "4920817"
## [1285] "23005" "68057" "1300490" "8923587" "4128732" "42053"
## [1291] "257724" "990491" "10216538" "7614130" "760628" "9881829"
## [1297] "2123381" "7671249" "3197865" "1351068" "5418675" "1889250"
## [1303] "183846" "230710" "5465624" "1534466" "14891223" "18985"
## [1309] "655067" "1385093" "2698348" "1125017" "9882639" "74673"
## [1315] "5387639" "2750410" "461137" "946926" "9305" "360630"
## [1321] "6074334" "8118880" "10424925" "37023" "422244" "98123"
## [1327] "21262" "118253" "141529" "70226" "2251012" "30253"
## [1333] "15763" "84911" "46416" "7196" "48256" "6427773"
## [1339] "25825" "55380" "148177" "3715656" "1841061" "101686"
## [1345] "275447" "174755" "4578476" "145353" "531458" "195558"
## [1351] "29940" "41975" "216675" "2311785" "165888" "541144"
## [1357] "1107310" "29168" "189773" "337752" "102107" "3093358"
## [1363] "42079" "240416" "32506" "70747" "358817" "15403"
## [1369] "38957" "214777" "100609" "1343866" "168717" "549720"
## [1375] "18996" "25094" "93033" "120592" "187972" "484981"
## [1381] "2055" "73539" "59017" "5829" "18621" "19922"
## [1387] "21119" "7412" "18125" "10795" "13004" "38207"
## [1393] "9394" "3883589" "2719142" "931595" "1480189" "2468063"
## [1399] "309176" "807338" "446434" "522466" "584126" "32551"
## [1405] "90218" "212524" "2045554" "745684" "416540" "16601"
## [1411] "3057481" "224514" "26247" "10055521" "21892" "197540"
## [1417] "29445" "1083571" "4230886" "2119218" "1327265" "1242855"
## [1423] "401425" "10979062" "515657" "955656" "1468591" "725897"
## [1429] "549039" "1559650" "292164" "520962" "1381820" "525517"
## [1435] "696" "194969" "327599" "3816799" "105620" "37139"
## [1441] "147791" "347883" "343263" "216849" "354373" "753043"
## [1447] "43055" "80678" "153381" "559" "3073251" "26649"
## [1453] "2151039" "306764" "280098" "26985" "1125438" "42145"
## [1459] "171448" "104303" "47644" "125647" "4355" "214878"
## [1465] "811040" "155186" "34494" "260651" "4638163" "234110"
## [1471] "48615" "14774" "12753" "33983" "20267" "5761"
## [1477] "11618" "12948" "11436" "2150" "382" "24936"
## [1483] "1109" "108795" "1455" "1024" "1014822" "86961"
## [1489] "7320" "269194" "18616" "11950" "4289" "11716"
## [1495] "3323" "36606" "328619" "46741" "530854" "7050"
## [1501] "17753" "520609" "432" "32029" "4207" "64"
## [1507] "96" "82471" "496" "29436" "19230" "11126"
## [1513] "23671" "9652" "9626" "29319" "1791" "9199"
## [1519] "14014" "110877" "10366" "530792" "12137" "6404"
## [1525] "6356" "169" "15246" "4076" "106750" "33785"
## [1531] "58795" "3235" "47031" "131" "673203" "2178"
## [1537] "175625" "8508" "3484" "379415" "19245" "24877"
## [1543] "10088" "3762" "141363" "472584" "1329192" "148295"
## [1549] "41273" "392596" "514088" "41867" "23060" "112080"
## [1555] "15489" "51895" "623398" "66661" "10447" "1574197"
## [1561] "19170" "169609" "6188" "1369" "2952" "9856"
## [1567] "10753" "154" "288523" "4522" "3328" "854"
## [1573] "560" "63186" "23772" "6007" "2903" "3063"
## [1579] "3234" "276" "1595" "879" "68559" "1123"
## [1585] "566" "97" "214" "248" "2195" "1615"
## [1591] "359" "38021" "6190" "13155" "1160" "59917"
## [1597] "1042" "253" "3396" "59729" "133117" "47213"
## [1603] "95537" "51838" "36028" "528745" "44062" "79667"
## [1609] "20763" "8126" "50887" "63160" "28737" "45579"
## [1615] "19720" "361970" "159619" "354384" "2376564" "129603"
## [1621] "1135" "578" "63" "216" "171" "45"
## [1627] "717" "2921" "92" "1361" "395" "79"
## [1633] "51" "576" "168" "163" "319" "133"
## [1639] "17" "726" "492" "41" "625" "59158"
## [1645] "19473" "73118" "27524" "102858" "2094" "33033"
## [1651] "78825" "18674" "6266" "22" "53743" "2657"
## [1657] "4476" "156410" "2006" "6099" "23160" "8348"
## [1663] "7837" "6185" "1838" "3707" "315" "87418"
## [1669] "21189" "1746" "69126" "453" "10710" "700"
## [1675] "914" "15875" "503" "488" "26862" "72167"
## [1681] "6035" "9945" "4318" "78" "2218" "47"
## [1687] "23889" "650" "3498" "3052" "1747" "1686"
## [1693] "529" "1388" "572" "2159" "2951" "15545"
## [1699] "5521" "2108" "408" "272" "4852" "90"
## [1705] "4303" "460" "513" "112" "83" "343"
## [1711] "137" "4107" "44" "124" "330" "531"
## [1717] "56" "123" "122" "3786" "65" "292"
## [1723] "19" "78158306" "66577313" "8606259" "49173" "2955326"
## [1729] "22492" "17014787" "4305441" "441189" "4831125" "4919"
## [1735] "13762" "6086" "70616" "1200" "76480" "271445"
## [1741] "225103" "33177" "54768" "457197" "25562" "16404"
## [1747] "2508" "79658" "374" "1259075" "4751" "60562"
## [1753] "22695" "22098" "231325" "13223" "479908" "313633"
## [1759] "540930" "57146" "1225339" "19583" "344921" "79129"
## [1765] "83488" "3781770" "315441" "382120" "412725" "3806669"
## [1771] "1259849" "486824" "1157004" "423105" "205803" "285816"
## [1777] "138026" "8936" "4253" "14835" "6388" "309872"
## [1783] "17955" "51502" "1064049" "58341" "637309" "161610"
## [1789] "19446" "1520959" "33249" "1175794" "852455" "900064"
## [1795] "3677" "695613" "207712" "175722" "2052" "624557"
## [1801] "522018" "141613" "6210998" "591312" "94294" "608753"
## [1807] "38961" "5916606" "441473" "2788923" "973270" "909226"
## [1813] "1573054" "857923" "35563" "85858" "106798" "8820"
## [1819] "37186" "25714" "44255" "1084945" "18252" "42750"
## [1825] "3656" "216741" "662287" "30834" "367290" "2588"
## [1831] "162655" "3860225" "125783" "171584" "244141" "568273"
## [1837] "142512" "109124" "135043" "108592" "1315242" "48732"
## [1843] "308234" "178497" "68406" "6012719" "45362" "18364"
## [1849] "15867" "9189" "23187" "11798" "9975" "52896"
## [1855] "7793" "9701" "31519" "181990" "213735" "42871"
## [1861] "315908" "210208" "1370749" "79261" "284725" "67071"
## [1867] "46153" "101883" "1659" "57920" "28523" "24953"
## [1873] "37253" "33758" "3420" "7193" "2278" "5121"
## [1879] "39735" "1558" "16966" "41986" "186116" "13085"
## [1885] "28560" "34171" "44588" "4158" "105773" "279428"
## [1891] "33583" "94205" "95520" "181798" "25719" "4602"
## [1897] "72596" "110425" "2375" "35497" "3878" "44071"
## [1903] "6380" "5123" "19232" "98716" "109500" "21159"
## [1909] "1320" "50424" "32398" "10858556" "219745" "38953"
## [1915] "142634" "259450" "123029" "914804" "21841" "5282578"
## [1921] "10349" "859" "40289" "3362" "49680" "3378"
## [1927] "10525" "3492" "654419" "1864" "74476" "221858"
## [1933] "401820" "3116" "31985" "4400" "3337956" "11677"
## [1939] "3158047" "125259" "56114" "15700" "16523" "26361"
## [1945] "285788" "4410" "5855" "47090" "233039" "28578"
## [1951] "1159058" "53421" "1579287" "116880" "21730" "62421"
## [1957] "70189" "847159" "251951" "240475" "527247" "55427"
## [1963] "68070" "2418135" "329160" "42677" "1517369" "811693"
## [1969] "23440" "3368649" "29707" "15098" "35724" "71898"
## [1975] "4865093" "106080" "44941" "129272" "111066" "49553"
## [1981] "43296" "130081" "462152" "140917" "88860" "49211"
## [1987] "351254" "157506" "1871416" "420973" "34753" "635846"
## [1993] "78140" "244371" "12865" "215343" "6120977" "753115"
## [1999] "16320" "852649" "1494491" "819774" "33439" "477831"
## [2005] "126337" "373606" "15426" "714340" "1451000" "1490732"
## [2011] "2163282" "1163232" "751766" "7594559" "1028637" "167652"
## [2017] "1075277" "7529865" "93726" "597068" "823109" "197295"
## [2023] "21578" "307453" "32896" "542561" "462702" "521138"
## [2029] "283662" "82882" "459795" "133825" "911995" "1733"
## [2035] "342909" "31908" "56270" "107724" "101455" "152780"
## [2041] "21733" "410384" "277902" "91031" "112725" "76346"
## [2047] "63938" "18678" "39878" "152867" "63580" "121003"
## [2053] "135763" "176448" "1981" "16016" "9992" "36490"
## [2059] "122282" "4011" "25172" "14123" "2487" "180938"
## [2065] "950" "232423" "1664" "1391" "2486" "188834"
## [2071] "697" "5510" "4549" "6106" "288809" "43611"
## [2077] "78442" "3017" "30840" "36255" "752" "926"
## [2083] "26102" "37167" "2020" "798" "7543" "1845"
## [2089] "13098" "1904" "11085" "3387" "11151" "29673"
## [2095] "50017" "63650" "50179" "9971" "1660" "361"
## [2101] "5305" "24082" "990" "32386" "35394" "28895"
## [2107] "11549" "34123" "4057" "5517" "4272" "666521"
## [2113] "838765" "2943" "108318" "68935" "80900" "75545"
## [2119] "1605267" "136626" "219848" "52029" "49190" "5150"
## [2125] "64713" "216388" "481545" "6012" "260121" "1830388"
## [2131] "17878" "26871" "1162837" "359403" "9235155" "33782"
## [2137] "192641" "2338655" "751551" "24781" "32862" "16101"
## [2143] "76779" "2129689" "98585" "459851" "5572" "16815"
## [2149] "45562" "285" "256" "21443" "2750" "7081"
## [2155] "17882" "421800" "43935" "171889" "251037" "15750"
## [2161] "27560" "150932" "928" "768833" "26665" "13275"
## [2167] "48930" "43054" "15680" "16980" "5112" "30447"
## [2173] "165299" "620534" "599872" "12564" "2528" "34"
## [2179] "427" "35560" "397422" "11182" "16734" "10035"
## [2185] "20313" "25740" "42546" "6925" "24281" "18039"
## [2191] "22748" "47780" "7705" "33256" "14544" "134895"
## [2197] "48082" "2419" "17915" "61776" "10323" "1609"
## [2203] "30403" "18622" "8258" "57573" "17202" "263525"
## [2209] "14114" "890" "7153" "149723" "6762" "120373"
## [2215] "40225" "42849" "5960" "18294" "38655" "8033493"
## [2221] "5745093" "18239" "24199" "37333" "12759663" "33216"
## [2227] "28860" "76604" "26189" "739329" "45838" "25592"
## [2233] "34126" "2394" "330468" "136874" "1236" "7790693"
## [2239] "537554" "315585" "12215" "127223" "9602" "24151"
## [2245] "45483" "28250" "1859115" "74819" "18513" "14552"
## [2251] "87055" "17030" "1280423" "357" "163997" "5431"
## [2257] "1420" "118439" "59973" "32111" "114788" "70404"
## [2263] "429580" "876866" "207706" "4254879" "111507" "472904"
## [2269] "115409" "166367" "618918" "192661" "54207" "60571"
## [2275] "1335799" "148506" "679912" "152692" "77311" "48211"
## [2281] "12388" "85387" "33509" "342336" "90831" "12718"
## [2287] "85659" "16395" "807" "24265" "1657" "576454"
## [2293] "88675" "56848" "19096" "1116393" "154578" "40676"
## [2299] "39833" "273283" "139480" "801054" "65597" "1107320"
## [2305] "4594198" "94427" "335115" "33926" "1028794" "134203"
## [2311] "15693" "48979" "410303" "63712" "10595" "9496"
## [2317] "428581" "225544" "3090727" "474439" "41137" "75336"
## [2323] "745245" "4934130" "137562" "172990" "68309" "1121805"
## [2329] "7146" "6466641" "49657" "1724" "139258" "32794"
## [2335] "102923" "6702776" "7583" "24215" "5073" "15633"
## [2341] "1141545" "29485" "142393" "71688" "114851" "62209"
## [2347] "202474" "512102" "298321" "5783441" "47393" "55525"
## [2353] "2267" "266401" "649568" "6342" "5413" "1237135"
## [2359] "4724" "43960" "3277209" "229" "6626" "10796"
## [2365] "273994" "29203" "18918" "2056" "440" "66453"
## [2371] "398" "12089" "2828" "89342" "495905" "86743"
## [2377] "30498" "97890" "25037" "58617" "62301" "37237"
## [2383] "1591" "595120" "100130" "294701" "63624" "112977"
## [2389] "58052" "12180" "118459" "112479" "69417" "733838"
## [2395] "157495" "86481" "77724" "2390185" "33074" "35771"
## [2401] "290241" "69488" "10401" "28806" "11343" "66730"
## [2407] "25807" "251616" "87300" "181399" "881" "40704"
## [2413] "624924" "51145" "647844" "2591941" "7435" "115773"
## [2419] "12008" "2084126" "536926" "3016297" "1188154" "2731171"
## [2425] "8226" "228794" "3252896" "226456" "1079491" "9653"
## [2431] "58675" "1038306" "287250" "480643" "27800" "691474"
## [2437] "2131" "5383985" "26559" "13500" "8550" "1861310"
## [2443] "23089" "6949" "858208" "815981" "102451" "56403"
## [2449] "115072" "19302" "1488396" "6572" "577059" "1092367"
## [2455] "618798" "209696" "1498393" "15368" "123412" "185632"
## [2461] "80847" "2764964" "41418" "549973" "6011" "25370"
## [2467] "74146" "176873" "404617" "10270" "155999" "56713"
## [2473] "117255" "298843" "72513" "205191" "73695" "144879"
## [2479] "49794" "609182" "979" "53015" "277794" "67523"
## [2485] "17415" "496399" "549900" "1508137" "244567" "2401017"
## [2491] "57033" "12321" "122424" "21507" "80581" "37204"
## [2497] "10643" "226295" "57904" "5157" "8985" "16349"
## [2503] "30291" "25985" "60840" "133573" "23393" "198051"
## [2509] "102594" "80119" "26919" "267189" "6850" "18669"
## [2515] "16420" "16149" "71432" "282460" "86" "17941"
## [2521] "76" "3614" "1413" "3789" "67" "107"
## [2527] "4976" "3248" "9293" "62386" "162" "1002"
## [2533] "498" "34336" "9073" "7505" "11501" "2715"
## [2539] "349" "806" "60" "824" "6668" "1940"
## [2545] "1025" "5343" "247" "970" "3182" "1528"
## [2551] "76795" "1558437" "159455" "2053404" "892" "981995"
## [2557] "11118" "178934" "11297" "15370" "18194" "40606"
## [2563] "133338" "36900" "1312037" "4184" "100994" "20008"
## [2569] "13426" "18773" "26941" "135337" "7623" "1422858"
## [2575] "21404" "2143" "189313" "89868" "309617" "3478"
## [2581] "24349" "22154" "17493" "15966" "2332" "29344"
## [2587] "67772" "634" "18425" "25655305" "7557" "59089"
## [2593] "1551" "12764" "54807" "259003" "121916" "400"
## [2599] "3930" "1032076" "239242" "193381" "7624" "19738"
## [2605] "259605" "18699" "98819" "53006" "436921" "351168"
## [2611] "1615596" "906384" "5639" "504823" "25922" "5555"
## [2617] "921868" "6449" "15874" "2093" "26421" "2689"
## [2623] "36969" "45744" "714665" "119202" "6474426" "6685"
## [2629] "28835" "13205" "1261" "1215" "169965" "38630"
## [2635] "249919" "158196" "42624" "26411" "296781" "30693"
## [2641] "83558" "6066" "293080" "54256" "355921" "37882"
## [2647] "190888" "948198" "9548" "1071" "11908" "185058"
## [2653] "697212" "978" "877635" "51684" "175110" "11667403"
## [2659] "357944" "735" "2543" "18818" "30287" "31504"
## [2665] "13950" "21147" "41490" "2090" "44274" "7006"
## [2671] "2959" "40167" "56807" "1284017" "4332" "10382"
## [2677] "413999" "66978" "66384" "17703" "32121" "350"
## [2683] "74425" "131028" "84957" "3311" "23158" "1380"
## [2689] "49259" "185884" "40975" "27104" "247992" "63647"
## [2695] "6105" "30722" "56524" "24790" "13169" "61692"
## [2701] "3684" "18976" "63020" "62740" "76677" "78154"
## [2707] "479594" "201737" "233305" "80368" "23292" "23641"
## [2713] "13217" "17240" "256680" "62465" "103074" "7232629"
## [2719] "15681" "53481" "104800" "50459" "43269" "56443"
## [2725] "4928420" "1421884" "3652" "126282" "14110" "18710"
## [2731] "22063" "286454" "15922" "652" "29768" "102248"
## [2737] "41225" "162049" "26014" "53562" "10562" "21589"
## [2743] "3682" "2909" "37937" "15865" "63920" "38375"
## [2749] "16657" "301413" "20605" "16094" "65590" "32225"
## [2755] "44348" "23279" "12572" "70556" "1240" "56471"
## [2761] "6939" "10218" "617477" "1688" "18857" "11838"
## [2767] "60838" "886418" "3720" "9951" "2398" "213340"
## [2773] "1805398" "94989" "10247" "730" "263454" "1728557"
## [2779] "39480" "1092337" "4257" "1221896" "152658" "14766"
## [2785] "1852384" "353342" "3053" "960726" "1703479" "8389714"
## [2791] "867920" "798522" "6760" "13118" "413609" "1117212"
## [2797] "305765" "154668" "98324" "47698" "133195" "17069"
## [2803] "145088" "46253" "111741" "49275" "29265" "85763"
## [2809] "2440695" "137198" "22191" "5637451" "31061" "12495"
## [2815] "512996" "800" "2349421" "50" "3039889" "1305050"
## [2821] "155" "3042" "14210" "291" "4487182" "668"
## [2827] "828489" "10053186" "472247" "4624" "1397944" "2890"
## [2833] "27275" "1531" "873" "901110" "1218" "88"
## [2839] "557" "2387" "42916526" "686" "8096" "499"
## [2845] "608" "707" "376" "109" "43" "2751"
## [2851] "452" "4115" "459" "306" "1971777" "305347"
## [2857] "408292" "1736105" "5091448" "2588730" "640974" "3058687"
## [2863] "4972230" "951" "1591129" "14026" "1013867" "762706"
## [2869] "2586261" "91171" "1076243" "15301" "10158" "4147718"
## [2875] "1168959" "4000433" "23682" "338449" "214265" "187892"
## [2881] "740" "15443" "94910" "63773" "1506783" "1354"
## [2887] "4082" "564759" "951413" "17350" "15209" "16257"
## [2893] "4660" "1476" "75951" "10374" "210534" "9400"
## [2899] "894435" "1302" "4551" "12726" "3213548" "3943"
## [2905] "1117" "607" "9433" "13096" "1671658" "6495"
## [2911] "20368" "5427" "76593" "183" "5559" "127"
## [2917] "4830407" "64884" "857215" "2065" "12683" "1034"
## [2923] "989344" "4116" "7715" "4710" "543" "89"
## [2929] "777" "415" "231" "517" "99290" "1960"
## [2935] "29544" "1786" "6181640" "145" "19816" "4031"
## [2941] "15439" "4108" "65914" "621" "3250" "681"
## [2947] "10426" "4140" "1752017" "178723" "2454" "19758"
## [2953] "3133" "7453" "4635" "8137" "1372013" "3032"
## [2959] "403911" "249308" "29864" "250257" "80987" "896118"
## [2965] "421000" "90082" "83875" "1838090" "307398" "2176"
## [2971] "56259" "705805" "339" "61264" "405824" "797"
## [2977] "81747" "609" "164" "98" "934" "2451136"
## [2983] "290" "9140" "1603" "1760" "1656808" "1017408"
## [2989] "1185" "4046" "1955" "19047" "9019" "4444"
## [2995] "6418" "2351" "42" "11263" "4304" "369"
## [3001] "264" "703" "696019" "45224" "576210" "6263"
## [3007] "1111915" "67410" "5677" "2965" "155276" "11535"
## [3013] "5525" "4251" "1185148" "90415" "2852" "1734"
## [3019] "222308" "556659" "1827212" "953894" "31538" "37234"
## [3025] "58820" "758780" "596" "1202" "718" "901"
## [3031] "167229" "2803" "202" "189" "234606" "128"
## [3037] "2538" "156862" "63680" "19727" "4719" "32597"
## [3043] "552" "166033" "960" "133180" "620" "817"
## [3049] "313" "37789" "3570" "48929" "89947" "466"
## [3055] "30630" "7462" "8600" "29505" "106" "6187"
## [3061] "659" "3965" "4656" "205" "1475" "148826"
## [3067] "354" "1699" "11393" "401530" "925" "671"
## [3073] "274" "140" "30443" "22401" "324" "14832"
## [3079] "2059" "826" "180697" "589" "428268" "298041"
## [3085] "29" "230" "2026" "86956" "1129" "108002"
## [3091] "213" "147" "3062845" "1162" "720" "502"
## [3097] "1486" "6627" "4383" "680" "24668" "13788"
## [3103] "26893" "591411" "2194" "2012" "32" "657"
## [3109] "4264" "21107" "3642" "495971" "697939" "7357"
## [3115] "944" "5369" "135" "1852" "6367" "259"
## [3121] "5682" "7687" "51068" "2925" "1655" "1696"
## [3127] "11244" "16771865" "14224" "5178" "628" "12435"
## [3133] "972574" "464900" "15097" "146913" "22503" "1503544"
## [3139] "5785" "334" "16111" "2789775" "482630" "69115"
## [3145] "38606" "3044" "1820" "10067" "480" "2300"
## [3151] "53144" "22775" "370" "41502" "963" "21592"
## [3157] "103" "138129" "6454" "17988" "1771" "8465"
## [3163] "146" "21943" "1468" "1088" "29756" "1057"
## [3169] "10490" "16600" "67611" "6601" "233588" "166886"
## [3175] "93638" "83977" "139" "784" "331" "655"
## [3181] "3315" "71" "1178" "2158" "245" "210"
## [3187] "568" "712" "24517" "468" "5599" "52"
## [3193] "11404" "10249" "906" "1011" "4575" "509"
## [3199] "93" "397147" "109263" "192677" "16876" "2113"
## [3205] "6121" "85578" "165723" "984451" "3546" "430643"
## [3211] "9879473" "4288" "2399" "582" "15924" "3283"
## [3217] "4016834" "903" "87" "594" "2772" "1997"
## [3223] "309" "2460" "1744" "1667" "856" "1704112"
## [3229] "2142" "2371543" "2447" "352097" "37607" "12121"
## [3235] "101957" "95080" "1130966" "124970" "1546" "1092106"
## [3241] "40617" "5754" "54063" "1166" "37584" "1925"
## [3247] "168487" "20418" "58366" "1216" "4210" "12147"
## [3253] "10806" "355837" "22018" "30515" "4878" "252"
## [3259] "63197" "32613" "514" "1714" "24210" "12736"
## [3265] "586" "44636" "3432" "10748" "916" "875"
## [3271] "1616" "18612" "2160" "5898" "38517" "5227"
## [3277] "281448" "1131937" "721646" "1499466" "285814" "351267"
## [3283] "16936" "74842" "45871" "5180480" "427185" "50771"
## [3289] "7464996" "4421" "337242" "387958" "229329" "97071"
## [3295] "853495" "5894" "96028" "295430" "121612" "367951"
## [3301] "1987" "650114" "605" "41444" "405" "3976"
## [3307] "201" "11258" "11408" "94661" "71829" "13604"
## [3313] "1721" "24198" "24697" "8537" "180" "29540"
## [3319] "63699" "1886" "253115" "55571" "384602" "227401"
## [3325] "596628" "69279" "18921" "1628" "3908" "2105"
## [3331] "2901" "2634605" "44939" "37224" "829753" "48253"
## [3337] "111" "2371" "5103" "630" "3846378" "533"
## [3343] "5967" "1218055" "793" "27501" "18604" "12906"
## [3349] "224" "40934" "537" "4786" "42529" "472"
## [3355] "29854" "3270" "402" "7816" "409" "362"
## [3361] "3043" "336" "383" "3263" "1041" "377"
## [3367] "448" "166" "114340" "66473" "1450" "1298"
## [3373] "332" "9514" "152470" "5107" "9221" "10369"
## [3379] "1586" "121113" "14491" "2976" "1075" "208"
## [3385] "8769" "3005" "9914" "1774" "705" "18751"
## [3391] "25243" "52677" "8696" "10672" "999" "204"
## [3397] "6267" "40241" "37302" "3252" "317" "457"
## [3403] "1555" "1828" "1343" "20178" "20476" "39495"
## [3409] "2171" "6973" "8100" "61746" "17263" "30002"
## [3415] "5262" "41759" "4569" "18277" "721" "1776"
## [3421] "8638" "1417" "8581" "74902" "6988" "804"
## [3427] "263" "238459" "17876" "4726" "194" "74531"
## [3433] "165224" "503757" "79792" "626366" "38055" "7479"
## [3439] "26530" "76484" "1450632" "61990" "94761" "52312"
## [3445] "4931562" "306652" "23453" "50893" "2215" "9013"
## [3451] "6738" "68" "375" "2931" "536" "1998"
## [3457] "1689" "45458" "486" "949" "80927" "116973"
## [3463] "3597" "25627" "40" "55313" "41624" "1891"
## [3469] "65766" "346681" "1407" "2975" "1564" "6750"
## [3475] "3873" "74744" "107441" "18893" "26916" "1031"
## [3481] "345" "585" "734" "165" "807226" "322"
## [3487] "23971" "145931" "243121" "33812" "82827" "803"
## [3493] "218451" "1291" "57400" "284670" "445756" "361780"
## [3499] "41608" "24456" "2319" "7878" "6696" "4832"
## [3505] "173394" "2654" "96419" "13620" "12322" "29551"
## [3511] "47463" "1340" "55011" "7116" "759" "497826"
## [3517] "1777" "518" "1201" "1133393" "3547" "1867"
## [3523] "208501" "4581" "1313" "1493" "4537" "5849"
## [3529] "327" "33944" "10256" "8004" "636228" "245839"
## [3535] "68072" "210317" "1333338" "899748" "23729" "406511"
## [3541] "179139" "104389" "559931" "130689" "234971" "228737"
## [3547] "72202" "2570" "14145" "21223" "438911" "2063"
## [3553] "45771" "7148" "19209" "29495" "1721943" "8219586"
## [3559] "690148" "579519" "170973" "62636" "123136" "250197"
## [3565] "221722" "29838" "1012" "183004" "143087" "652940"
## [3571] "336386" "5195" "91935" "92522" "45370" "41269"
## [3577] "394842" "1008012" "1231" "1443" "148083" "31596"
## [3583] "598975" "64164" "16063" "684" "177" "188"
## [3589] "11018" "676" "70" "242" "3743" "129409"
## [3595] "22667" "10114" "48427" "4704" "265" "41000"
## [3601] "161637" "349151" "169369" "218881" "31134" "242722"
## [3607] "244039" "720685" "84389" "137696" "322976" "254"
## [3613] "898" "22435" "16801" "391325" "28735" "580160"
## [3619] "862" "1226514" "19070" "20247" "1363" "1602"
## [3625] "1017237" "211" "410" "1745" "469" "25195"
## [3631] "9636" "153" "1152" "36268" "20879" "76340"
## [3637] "2563" "4374" "23966" "961" "246201" "125652"
## [3643] "11379" "2057" "42329" "344283" "258717" "40437"
## [3649] "51787" "531074" "480208" "29867" "450013" "228130"
## [3655] "155693" "81668" "11773" "870928" "407788" "118285"
## [3661] "326232" "318134" "2445" "65119" "34898" "889425"
## [3667] "1041836" "17945" "47151" "107765" "37165" "174127"
## [3673] "4706" "73919" "532" "344819" "9335" "100805"
## [3679] "23168" "2628" "235486" "2717" "24123" "7728"
## [3685] "2180" "59223" "16162" "1976" "6698" "21266"
## [3691] "4041" "2691" "27856" "9126" "568922" "85278"
## [3697] "16521" "91667" "664" "2433" "1827" "762"
## [3703] "23609" "24312" "874" "29462" "159063" "294"
## [3709] "6207063" "631" "617" "215" "1275373" "1434"
## [3715] "701" "2420" "251" "1170641" "150" "2598579"
## [3721] "574719" "78629" "648380" "7317" "18325" "725"
## [3727] "7718" "249" "29062" "484" "1948" "35572"
## [3733] "20973" "1604146" "260137" "2079" "8346" "7264"
## [3739] "6205" "19666" "2808" "24775" "3845" "244"
## [3745] "15765" "305" "141" "4546" "924" "569"
## [3751] "15806" "94" "6344" "10446" "1213" "649"
## [3757] "72" "489" "2954" "9895" "162530" "39779"
## [3763] "254518" "88901" "65146" "104551" "66321" "29270"
## [3769] "751911" "1520" "11087" "26426" "2728" "132"
## [3775] "463" "386" "5300" "226" "1491" "592"
## [3781] "181" "690" "677" "79826" "3647" "242096"
## [3787] "3452530" "1424" "169661" "172" "7441" "36151"
## [3793] "113" "8343" "209" "27135" "6230" "137377"
## [3799] "7461" "39109" "5988" "10341" "193" "289"
## [3805] "540" "4496" "1238" "474" "4071" "3347"
## [3811] "983" "1988" "3491" "4396" "192851" "8418"
## [3817] "9443" "787" "838" "2806" "66033" "54090"
## [3823] "3103" "48545" "3451011" "618562" "4330" "484226"
## [3829] "28390" "1580" "556929" "2520" "559597" "305367"
## [3835] "128367" "103909" "76608" "275843" "263907" "1849"
## [3841] "3066" "262" "28892" "634159" "428" "1542"
## [3847] "17067" "3322" "2509" "447" "29798" "412"
## [3853] "407" "1073" "63056" "643" "81219" "694"
## [3859] "35188" "31883" "101762" "28660" "20101" "10440"
## [3865] "267378" "2017" "142693" "2076" "7118" "34079"
## [3871] "4334" "1644" "1630" "10758" "9612" "5442"
## [3877] "205830" "3049" "867" "14453" "6079" "167406"
## [3883] "128579" "389" "8175" "8114" "4027" "17180"
## [3889] "286" "675" "219" "577" "7420" "5055"
## [3895] "3640" "1819" "2312084" "282" "284795" "5644"
## [3901] "63765" "1118201" "899010" "205914" "1042170" "42729"
## [3907] "29944" "212067" "155694" "344383" "4099" "4722"
## [3913] "501" "616" "4010" "325" "35121" "341"
## [3919] "381023" "26601" "414" "68664" "524467" "52199"
## [3925] "6333" "956" "969" "1469" "2066" "26744"
## [3931] "802" "41747" "19221" "2448" "5793284" "549"
## [3937] "445" "301" "222" "4160" "2614" "2683"
## [3943] "3379" "33783" "28447" "8419" "4205" "1563"
## [3949] "355" "1901" "6073" "7326" "1318" "855"
## [3955] "320" "9765" "2710" "622" "1879" "8827"
## [3961] "11760" "328" "8185" "661" "2539" "913"
## [3967] "597" "33661" "46801" "5591653" "1432447" "1167143"
## [3973] "125578" "14283" "20675" "51569" "38297" "159398"
## [3979] "776730" "152" "70903" "4451317" "66740" "186"
## [3985] "7808" "174423" "5661" "157" "2256" "2526"
## [3991] "5004" "191" "67186" "8259" "3068" "13466"
## [3997] "27749" "25515" "28030" "75719" "1103" "21804"
## [4003] "20691" "232" "5865" "544" "2068" "1902"
## [4009] "1418" "2736" "1016" "1304467" "1167" "245104"
## [4015] "5879" "138337" "947515" "5546" "13304" "4585"
## [4021] "9966" "70335" "269" "11480" "1895" "847"
## [4027] "19640" "333" "25205" "48451" "15665" "3703"
## [4033] "2794" "632" "1307" "641219" "1926" "437"
## [4039] "20829" "11187" "2992" "636" "21979" "37122"
## [4045] "22167" "238" "2838064" "4015" "698" "15057"
## [4051] "10198" "132792" "4977" "45558" "19784" "10006"
## [4057] "246705" "2719" "547" "329" "2839" "2048"
## [4063] "1376" "84114" "13064" "551" "38448" "22782"
## [4069] "85882" "51067" "13005" "396" "41693" "138739"
## [4075] "91645" "107497" "20535" "7664" "25952" "51791"
## [4081] "25744" "54221" "2231" "412744" "12784" "2586"
## [4087] "992" "24557" "16041" "267229" "55723" "14356"
## [4093] "997" "23474" "12293" "3588" "767" "1279"
## [4099] "22290" "34279" "7342" "5706" "183343" "5481"
## [4105] "769" "45452" "112223" "2100" "12034" "1977"
## [4111] "62561" "9016" "41625" "8433" "421" "555"
## [4117] "19212" "31621" "688" "7000" "5463" "17998"
## [4123] "21785" "1308" "4538" "522" "201426" "26138"
## [4129] "51523" "6477" "1008" "1692" "1143" "3433"
## [4135] "4923" "885187" "113951" "658087" "4901" "2132"
## [4141] "175" "1432809" "293" "51366" "170" "7314"
## [4147] "116" "2746" "4379" "3146" "179" "14153"
## [4153] "21866" "11514" "9950" "1045" "51110" "17861"
## [4159] "1647" "271" "1947" "4928" "13232" "1691"
## [4165] "108" "5509" "1623" "235" "2599" "52390"
## [4171] "4218587" "288835" "221" "29330" "29990" "348962"
## [4177] "1995" "2099" "1022" "4074" "154519" "207"
## [4183] "12414" "401643" "9898" "3371" "39038" "9403"
## [4189] "17372" "7885" "1364" "155649" "562" "206602"
## [4195] "219821" "1415" "144545" "349503" "20001" "2480"
## [4201] "10774" "5025" "5618" "2233681" "385764" "151095"
## [4207] "488039" "24900999" "23802" "2246379" "85496" "262076"
## [4213] "71740" "3341" "843" "2889" "112482" "3989"
## [4219] "8190074" "85079" "953790" "10093" "1500" "1873"
## [4225] "1147" "1264" "246" "7519" "2910" "373"
## [4231] "6271" "24226" "2359" "1985" "3863" "20463"
## [4237] "920571" "2263" "5395" "30444" "256916" "37513"
## [4243] "40847" "96045" "21433" "82005" "120035" "6386"
## [4249] "43314" "24628" "39698" "121533" "10776" "13519"
## [4255] "39153" "51973" "48754" "7046" "773" "117461"
## [4261] "108336" "3904" "14563" "17786" "709" "81001"
## [4267] "581" "32416" "8038" "420" "6947" "26572"
## [4273] "248417" "102215" "15911" "9465" "4607" "92958"
## [4279] "1018" "7935" "132282" "2548" "34443" "36557"
## [4285] "475020" "59152" "2871" "19207" "1044" "28237"
## [4291] "3247" "119368" "4552" "108130" "293086" "8778"
## [4297] "695" "7063" "37975" "117850" "167974" "2630"
## [4303] "4756" "323" "14754" "7389" "92010" "68226"
## [4309] "3446" "297" "3106" "6078" "561" "77717"
## [4315] "40328" "1502622" "22773" "26358" "52163" "299046"
## [4321] "41089" "1019" "2328" "433" "4946" "16459"
## [4327] "14823" "8668" "112565" "14604" "3253" "431"
## [4333] "3988" "8191" "693" "347" "853" "6208"
## [4339] "2374" "3661" "1992" "922" "4290" "495"
## [4345] "28136" "12667" "40907" "475944" "115176" "121082"
## [4351] "15830" "3757" "9555" "770" "2147" "3972"
## [4357] "2303" "20921" "27820" "11310" "715" "593"
## [4363] "416" "6997" "996" "2555" "165656" "3935"
## [4369] "12204" "29229" "31552" "12639" "1436" "4513"
## [4375] "6784" "268" "1137" "3069" "20843" "137674"
## [4381] "50428" "1419" "4069" "439" "818" "6060"
## [4387] "75140" "387" "16851" "541732" "47340" "81502"
## [4393] "208543" "85015" "2250" "6200" "11179" "1514"
## [4399] "470" "876" "32014" "1189" "2802" "1740"
## [4405] "1372" "15753" "1641" "4228" "9307" "1151"
## [4411] "12400" "528550" "35337" "2674051" "766" "122010"
## [4417] "136540" "134412" "327914" "38824" "171017" "6289"
## [4423] "49523" "260527" "419375" "2464" "93898" "42190"
## [4429] "420518" "39895" "794058" "119685" "88993" "6514"
## [4435] "954" "355613" "504765" "2440877" "6715" "2557"
## [4441] "937" "139545" "22333" "45651" "16190" "304106"
## [4447] "1186" "258" "264755" "2354042" "6895" "1440"
## [4453] "186648" "226541" "74497" "264260" "50109" "54034"
## [4459] "47386" "401211" "498894" "9149" "191621" "32849"
## [4465] "251686" "252006" "28694" "785622" "113183" "951435"
## [4471] "45610" "257531" "198480" "375996" "152102" "17108"
## [4477] "1764" "3408" "11100" "1648" "65448" "16678"
## [4483] "10318" "53301" "195" "10786" "407589" "104068"
## [4489] "562345" "3941129" "314774" "1878" "78142" "326042"
## [4495] "35172" "28633" "331692" "3527" "151" "1130"
## [4501] "6450" "29387" "38767" "5623" "157997" "83545"
## [4507] "34062" "1484" "152395" "3715" "975" "396090"
## [4513] "466495" "41683" "96658" "227798" "303394" "39068"
## [4519] "3909032" "6026" "41331" "28107" "217736" "1648515"
## [4525] "55952" "928720" "609186" "771001" "617732" "332623"
## [4531] "371318" "216513" "696665" "860078" "5997" "796"
## [4537] "2013" "21095" "429" "1387" "6752" "708"
## [4543] "19388" "851" "6505" "569727" "91186" "1072565"
## [4549] "120494" "637" "43677" "79132" "39682" "18478"
## [4555] "32879" "34612" "253207" "23348" "46242" "40467"
## [4561] "16192" "148715" "24565" "59632" "8780" "38607"
## [4567] "942" "5985" "426" "505" "794" "905"
## [4573] "820" "11872" "69013" "364013" "13079" "4856"
## [4579] "3745" "2032" "456474" "267395" "45359" "25427"
## [4585] "14432" "54520" "253155" "154108" "72161" "43088"
## [4591] "6320" "271214" "14089" "26452" "6120" "7801"
## [4597] "57449" "7566" "4649" "10484" "2537" "4441"
## [4603] "86172" "7969" "56664" "2295" "1290" "15618"
## [4609] "11402" "1007" "8193" "1115" "1853" "1283"
## [4615] "4813" "3003" "666" "12111" "8432" "7812"
## [4621] "9659" "2576" "3358" "1911" "28140" "5485"
## [4627] "11250" "5093" "8450" "13492" "2362" "139432"
## [4633] "1638" "7896" "58575" "32881" "441" "475369"
## [4639] "358633" "1094094" "23347" "1626" "36578" "14253"
## [4645] "15829" "101738" "372553" "6716" "3345" "200450"
## [4651] "42182" "2700" "2310" "594406" "85317" "1013"
## [4657] "2311" "97209" "4518" "3580" "11748" "1205"
## [4663] "138872" "1091" "11788" "23022" "3725" "1357"
## [4669] "19291" "87766" "14002" "22896" "107778" "10676"
## [4675] "2596" "71852" "4908" "7335" "12443" "2046"
## [4681] "3227" "368" "2962" "768" "21423" "22382"
## [4687] "877576" "22032" "162933" "477" "190086" "63779"
## [4693] "1312936" "783025" "4328" "137338" "199739" "6231"
## [4699] "24985" "7578" "13479633" "436615" "465831" "67707"
## [4705] "4847" "21762" "20941" "93930" "5174" "935"
## [4711] "19234" "7605" "73821" "12993" "868" "14051"
## [4717] "4595" "3390" "500" "23599" "101163" "321"
## [4723] "128808" "1048766" "1251479" "5692" "6827" "1522"
## [4729] "17671" "902" "21186" "18298" "298" "3375"
## [4735] "6697" "6156" "5964" "3195" "281" "15068"
## [4741] "449" "1894" "1763" "120852" "2807" "2318"
## [4747] "2058" "10355" "3606" "1060" "417" "580"
## [4753] "2371338" "1690802" "3344300" "1455952" "282727" "636995"
## [4759] "567632" "1461698" "69574" "32344" "199808" "203101"
## [4765] "56444" "201631" "32600" "93870" "222664" "166251"
## [4771] "70389" "172281" "567984" "820577" "32496" "2903386"
## [4777] "85484" "4490" "38419" "42767" "140658" "33178"
## [4783] "585564" "1172" "2915" "318142" "5341" "1111"
## [4789] "627" "3429" "1730" "30350" "55408" "633"
## [4795] "1611" "3776" "4114" "403" "2210" "1242"
## [4801] "435" "5969" "311" "22165" "883" "6547"
## [4807] "42497" "24278" "7993" "1309728" "3946" "17453"
## [4813] "14773" "2282" "8369" "1506" "30008" "11002"
## [4819] "47576" "2533" "1880" "7379" "20977" "13388"
## [4825] "35746" "137167" "7203" "267636" "1294" "234"
## [4831] "16073" "64815" "5075" "125616" "3593" "32522"
## [4837] "1036" "27130" "157264" "157322" "76627" "5290"
## [4843] "1094" "326689" "6969" "138050" "105766" "80313"
## [4849] "4231" "42515" "20620" "4600" "9051" "14692"
## [4855] "40678" "59096" "127810" "27179" "351607" "81543"
## [4861] "31970" "366" "13731" "104583" "58553" "6669"
## [4867] "764967" "5339" "6735" "23104" "13258" "48731"
## [4873] "8482" "3356" "13714" "35989" "16237" "21149"
## [4879] "20292" "140883" "16426" "32812" "8091" "352"
## [4885] "3048" "3136" "467" "34417" "5482" "1961"
## [4891] "697805" "182363" "192374" "4871" "4234" "49210"
## [4897] "6667" "31705" "94308" "848" "751" "595"
## [4903] "6133" "840" "8011" "2436" "20421" "5933"
## [4909] "36968" "3654" "23302" "1914" "23805" "526595"
## [4915] "279917" "4254" "161423" "2536" "56197" "80904"
## [4921] "207440" "93608" "244797" "7904" "3175" "1123190"
## [4927] "49381" "2102" "7972" "4416" "3543" "190274"
## [4933] "2850" "12846" "2714" "6143" "32831" "2941"
## [4939] "197979" "2208" "1986068" "71468" "910051" "6673"
## [4945] "114479" "1489" "8608" "14989" "7107" "127831"
## [4951] "211308" "382100" "1317" "200" "291941" "187200"
## [4957] "246538" "177542" "26202" "750321" "6577" "711719"
## [4963] "47069" "922752" "7243" "57076" "7881" "44233"
## [4969] "291901" "121304" "5118" "24175" "135739" "162831"
## [4975] "10773" "61600" "75566" "384368" "71328" "15105"
## [4981] "34514" "151374" "2062" "50060" "188740" "43852"
## [4987] "13330" "46369" "29155" "2200" "5449" "5731"
## [4993] "11023" "5291" "39661" "8014" "141515" "254861"
## [4999] "19601" "1938" "519" "1652" "39647" "12781"
## [5005] "980" "3482" "2801" "173" "2936" "2510"
## [5011] "4798" "1909" "175509" "10449" "230564" "81614"
## [5017] "171771" "5867" "32207" "23859" "14428" "4737"
## [5023] "7851" "20865" "77609" "11449" "940" "3509"
## [5029] "380" "669901" "7252" "337532" "584070" "1553"
## [5035] "1303" "93708" "24980" "1877" "932870" "24137"
## [5041] "1536512" "398746" "70883" "163679" "1719" "201718"
## [5047] "49971" "1260143" "522205" "174215" "112384" "108169"
## [5053] "1260903" "95201" "223941" "444" "442" "1865"
## [5059] "66894" "214923" "606" "43045" "4501" "891"
## [5065] "20807" "2649" "2558" "6747" "5886" "17543"
## [5071] "36813" "9389" "59660" "2338" "2822" "539931"
## [5077] "2223" "1032" "2233" "13752" "903392" "9513"
## [5083] "27557" "127229" "3071" "728" "2000" "256219"
## [5089] "900" "24091" "70105" "13253" "84779" "83891"
## [5095] "25489" "2294" "568391" "77585" "9699" "28728"
## [5101] "111634" "2645" "8723" "2115" "2695" "28151"
## [5107] "1092" "18280" "11510" "3258" "1550" "8894"
## [5113] "70351" "60298" "171220" "5474" "1327" "499483"
## [5119] "239" "19877" "58387" "54082" "497" "7443"
## [5125] "3674" "43191" "936" "32112" "6801" "2187"
## [5131] "280" "1276" "1461" "626" "18926" "3344"
## [5137] "789" "3696" "7300" "6849" "260" "2412"
## [5143] "3187" "1212" "9716" "201537" "11051" "38826"
## [5149] "264282" "15070" "100179" "318867" "172373" "25438"
## [5155] "283823" "3895" "9562" "42621" "710" "10743"
## [5161] "76498" "37090" "6396" "5285" "68025" "3047"
## [5167] "9606" "3840" "1905" "15221" "1749" "5229"
## [5173] "342" "670" "37140" "761" "974" "795"
## [5179] "2019" "758590" "15883" "401" "91397" "1526"
## [5185] "5675" "5015" "41074" "2317" "981" "729"
## [5191] "4354" "1463" "13819" "2378" "3704" "1539"
## [5197] "20755" "407694" "38487" "8649" "43645" "44027"
## [5203] "83671" "85410" "839206" "20364" "1228" "26347"
## [5209] "71476" "995002" "29415" "79464" "72522" "2980"
## [5215] "28429" "60097" "3502" "9296" "12257" "12919"
## [5221] "8122" "221691" "320334" "73185" "18584" "687136"
## [5227] "1063" "2027" "26545" "70753" "21735" "2917"
## [5233] "83427" "615" "424" "15036" "4838" "481"
## [5239] "37277" "13469" "2390" "479" "3673" "691"
## [5245] "1711" "346" "2372" "42432" "30668" "26224"
## [5251] "105954" "38473" "452589" "2183" "156322" "35171"
## [5257] "2505" "660613" "22570" "16282" "103199" "33788"
## [5263] "1517" "129542" "12700" "301895" "1211" "25275"
## [5269] "1456" "47688" "871" "1481" "148" "1338"
## [5275] "340" "763" "1566" "14221" "1351833" "3023"
## [5281] "11460" "88941" "11235" "2207" "85468" "36183"
## [5287] "55014" "275048" "1916" "1519671" "153176" "7279"
## [5293] "61392" "3471" "68358" "162564" "9183" "111809"
## [5299] "26252" "271908" "332083" "121321" "3268" "9894"
## [5305] "316378" "8484" "2531" "422" "404" "939"
## [5311] "834117" "245455" "455" "1035" "1287" "21661"
## [5317] "28510" "7339" "61445" "32433" "2036" "56496"
## [5323] "376223" "785" "5775" "885" "88486" "603"
## [5329] "1195" "398307"print(unique_values1)## [1] 4.100000 3.900000 4.700000 4.500000 4.300000 4.400000 3.800000 4.200000
## [9] 4.600000 3.200000 4.000000 4.173243 4.800000 4.900000 3.600000 3.700000
## [17] 3.300000 3.400000 3.500000 3.100000 5.000000 2.600000 3.000000 1.900000
## [25] 2.500000 2.800000 2.700000 1.000000 2.900000 2.300000 2.200000 1.700000
## [33] 2.000000 1.800000 2.400000 1.600000 2.100000 1.400000 1.500000 1.200000Change the column reviews from Str to int
## 'data.frame': 9659 obs. of 13 variables:
## $ App : chr "Photo Editor & Candy Camera & Grid & ScrapBook" "Coloring book moana" "U Launcher Lite – FREE Live Cool Themes, Hide Apps" "Sketch - Draw & Paint" ...
## $ Category : chr "ART_AND_DESIGN" "ART_AND_DESIGN" "ART_AND_DESIGN" "ART_AND_DESIGN" ...
## $ Rating : num 4.1 3.9 4.7 4.5 4.3 4.4 3.8 4.1 4.4 4.7 ...
## $ Reviews : num 159 967 87510 215644 967 ...
## $ Size : num 19 14 8.7 25 2.8 5.6 19 29 33 3.1 ...
## $ Installs : num 1e+04 5e+05 5e+06 5e+07 1e+05 5e+04 5e+04 1e+06 1e+06 1e+04 ...
## $ Type : chr "Free" "Free" "Free" "Free" ...
## $ Price : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Content.Rating: chr "Everyone" "Everyone" "Everyone" "Teen" ...
## $ Genres : chr "Art & Design" "Art & Design;Pretend Play" "Art & Design" "Art & Design" ...
## $ Last.Updated : chr "January 7, 2018" "January 15, 2018" "August 1, 2018" "June 8, 2018" ...
## $ Current.Ver : chr "1.0.0" "2.0.0" "1.2.4" "Varies with device" ...
## $ Android.Ver : chr "4.0.3 and up" "4.0.3 and up" "4.0.3 and up" "4.2 and up" ...| App | Category | Rating | Reviews | Size | Installs | Type | Price | Content.Rating | Genres | Last.Updated | Current.Ver | Android.Ver | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Min | Length:9659 | Length:9659 | Min. :1.000 | Min. : 0 | Min. : 0.0085 | Min. :0.000e+00 | Length:9659 | Min. : 0.000 | Length:9659 | Length:9659 | Length:9659 | Length:9659 | Length:9659 |
| Q1 | Class :character | Class :character | 1st Qu.:4.000 | 1st Qu.: 25 | 1st Qu.: 5.3000 | 1st Qu.:1.000e+03 | Class :character | 1st Qu.: 0.000 | Class :character | Class :character | Class :character | Class :character | Class :character |
| Median | Mode :character | Mode :character | Median :4.200 | Median : 967 | Median : 13.1000 | Median :1.000e+05 | Mode :character | Median : 0.000 | Mode :character | Mode :character | Mode :character | Mode :character | Mode :character |
| Mean | NA | NA | Mean :4.173 | Mean : 216593 | Mean : 20.1512 | Mean :7.778e+06 | NA | Mean : 1.099 | NA | NA | NA | NA | NA |
| Q3 | NA | NA | 3rd Qu.:4.500 | 3rd Qu.: 29401 | 3rd Qu.: 27.0000 | 3rd Qu.:1.000e+06 | NA | 3rd Qu.: 0.000 | NA | NA | NA | NA | NA |
| Max | NA | NA | Max. :5.000 | Max. :78158306 | Max. :100.0000 | Max. :1.000e+09 | NA | Max. :400.000 | NA | NA | NA | NA | NA |
There are 1463 missing values in rating.
As it could observed the Family category apps have the highest NA values. Let’s not drop them but handle them by replacing with the mean value for the category.
Checking for Outliers For rating by seeing frequency for each rating
breaks = seq(15,20,by = 1)
frequency_table = table(data_clean$Rating)
frequency_table##
## 1 1.2 1.4 1.5
## 16 1 3 3
## 1.6 1.7 1.8 1.9
## 4 8 8 11
## 2 2.1 2.2 2.3
## 12 8 14 20
## 2.4 2.5 2.6 2.7
## 19 20 24 23
## 2.8 2.9 3 3.1
## 40 45 81 69
## 3.2 3.3 3.4 3.5
## 63 100 126 156
## 3.6 3.7 3.8 3.9
## 167 224 286 359
## 4 4.1 4.17324304538799 4.2
## 513 621 1463 810
## 4.3 4.4 4.5 4.6
## 897 895 848 683
## 4.7 4.8 4.9 5
## 442 221 85 271From above it can be seen all the rating are between 1 and 5.But, most of them are above 4
Replacing NA values in Rating with mean
#Replace NA in Ratings with Overall Mean
data_clean <- data_clean %>%
mutate(Rating = ifelse(is.na(Rating), mean(Rating, na.rm = TRUE), Rating))
xkablesummary(data_clean)| App | Category | Rating | Reviews | Size | Installs | Type | Price | Content.Rating | Genres | Last.Updated | Current.Ver | Android.Ver | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Min | Length:9659 | Length:9659 | Min. :1.000 | Min. : 0 | Min. : 0.0085 | Min. :0.000e+00 | Length:9659 | Min. : 0.000 | Length:9659 | Length:9659 | Length:9659 | Length:9659 | Length:9659 |
| Q1 | Class :character | Class :character | 1st Qu.:4.000 | 1st Qu.: 25 | 1st Qu.: 5.3000 | 1st Qu.:1.000e+03 | Class :character | 1st Qu.: 0.000 | Class :character | Class :character | Class :character | Class :character | Class :character |
| Median | Mode :character | Mode :character | Median :4.200 | Median : 967 | Median : 13.1000 | Median :1.000e+05 | Mode :character | Median : 0.000 | Mode :character | Mode :character | Mode :character | Mode :character | Mode :character |
| Mean | NA | NA | Mean :4.173 | Mean : 216593 | Mean : 20.1512 | Mean :7.778e+06 | NA | Mean : 1.099 | NA | NA | NA | NA | NA |
| Q3 | NA | NA | 3rd Qu.:4.500 | 3rd Qu.: 29401 | 3rd Qu.: 27.0000 | 3rd Qu.:1.000e+06 | NA | 3rd Qu.: 0.000 | NA | NA | NA | NA | NA |
| Max | NA | NA | Max. :5.000 | Max. :78158306 | Max. :100.0000 | Max. :1.000e+09 | NA | Max. :400.000 | NA | NA | NA | NA | NA |
Now there are no missing values in reviews.
Category
# Checking the type of the Category
typeof(data_apps$Category)## [1] "character"length(unique(data_clean$Category))## [1] 33length(unique(data_clean$Genres))## [1] 118There are 33 categories in the the data frame with 118 genres. This means that in each category, there are multiple genres. Given that, the later analyses in this project can be proceeded with Category variable.
Below is the graph for the distribution of Categories for the dataset after removing duplicates.
Current Version & Genres
Due to the inconsistent formatting of values in the
Current.Ver column, this column is dropped and will be
excluded from the analysis.
data_final <- data_clean %>% select(-c('Genres', 'Current.Ver'))
data_final$Category <- as.factor(data_final$Category)
data_final$Android.Ver <- as.factor(data_final$Android.Ver)Content Rating, Last Updated
# Remove leading and trailing spaces and convert all text to a consistent format
data_final$Content.Rating <- trimws(tolower(data_final$Content.Rating))
cr_missing <- sum(is.na(data_final$`Content Rating`))
print(paste("Number of missing values in 'Content Rating':", cr_missing))## [1] "Number of missing values in 'Content Rating': 0"There are no missing values for Content rating.
# Convert Last Updated to Date format
data_final$Last.Updated <- as.Date(data_final$Last.Updated, format = "%B %d, %Y")
# Verify the cleaning
print("\nSummary of Last.Updated after cleaning:")## [1] "\nSummary of Last.Updated after cleaning:"print(summary(data_clean$Last.Updated))## Length Class Mode
## 9659 character characterAfter cleaning the Data
str(data_final)## 'data.frame': 9659 obs. of 11 variables:
## $ App : chr "Photo Editor & Candy Camera & Grid & ScrapBook" "Coloring book moana" "U Launcher Lite – FREE Live Cool Themes, Hide Apps" "Sketch - Draw & Paint" ...
## $ Category : Factor w/ 33 levels "ART_AND_DESIGN",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Rating : num 4.1 3.9 4.7 4.5 4.3 4.4 3.8 4.1 4.4 4.7 ...
## $ Reviews : num 159 967 87510 215644 967 ...
## $ Size : num 19 14 8.7 25 2.8 5.6 19 29 33 3.1 ...
## $ Installs : num 1e+04 5e+05 5e+06 5e+07 1e+05 5e+04 5e+04 1e+06 1e+06 1e+04 ...
## $ Type : chr "Free" "Free" "Free" "Free" ...
## $ Price : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Content.Rating: chr "everyone" "everyone" "everyone" "teen" ...
## $ Last.Updated : Date, format: "2018-01-07" "2018-01-15" ...
## $ Android.Ver : Factor w/ 34 levels "1.0 and up","1.5 and up",..: 16 16 16 19 21 9 16 19 11 16 ...Data Exploring and Visualization
Visualization for Price Distribution
# Count Plot for the Price distribution
ggplot(data_final, aes(x=Price)) +
geom_histogram(binwidth=2, fill="pink", color="black") +
xlim(0, 500) + ylim(0, 500) +
labs(title="Price Distribution", x="Price", y="Frequency") +
theme_minimal()
The data is highly skewed as there are many zero price entries.
# Boxplot for the same
ggplot(data_final, aes(y=Price)) +
geom_boxplot(outlier.colour = "red", outlier.shape = 16, outlier.size = 1, fill="pink", color="black") +
labs(title="Price Boxplot", y="Price") +
theme_minimal()
Checking outliers for Price
outlierKD2 <- function(df, var, rm = FALSE, boxplt = FALSE, histogram = TRUE, qqplt = FALSE) {
dt <- df # Duplicate the dataframe for potential alteration
var_name <- eval(substitute(var), eval(dt))
na1 <- sum(is.na(var_name))
m1 <- mean(var_name, na.rm = TRUE)
colTotal <- boxplt + histogram + qqplt # Calculate the total number of charts to be displayed
par(mfrow = c(2, max(2, colTotal)), oma = c(0, 0, 3, 0)) # Adjust layout for plots
# Q-Q plot with custom title
if (qqplt) {
qqnorm(var_name, main="Q-Q plot without Outliers")
qqline(var_name)
}
# Histogram with custom title
if (histogram) {
hist(var_name,main = "Histogram without Outliers", xlab = NA, ylab = NA)
}
# Box plot with custom title
if (boxplt) {
boxplot(var_name, main= "Box Plot without Outliers")
}
# Identify outliers
outlier <- boxplot.stats(var_name)$out
mo <- mean(outlier)
var_name <- ifelse(var_name %in% outlier, NA, var_name)
# Q-Q plot without outliers
if (qqplt) {
qqnorm(var_name, main="Q-Q plot with Outliers")
qqline(var_name)
}
# Histogram without outliers
if (histogram) {
hist(var_name, main = "Histogram with Outliers", xlab = NA, ylab = NA)
}
# Box plot without outliers
if (boxplt) {
boxplot(var_name, main = "Boxplot with Outliers")
}
# Add the title for the overall plot section if any plots are displayed
if (colTotal > 0) {
title("Outlier Check", outer = TRUE)
na2 <- sum(is.na(var_name))
cat("Outliers identified:", na2 - na1, "\n")
cat("Proportion (%) of outliers:", round((na2 - na1) / sum(!is.na(var_name)) * 100, 1), "\n")
cat("Mean of the outliers:", round(mo, 2), "\n")
cat("Mean without removing outliers:", round(m1, 2), "\n")
cat("Mean if we remove outliers:", round(mean(var_name, na.rm = TRUE), 2), "\n")
}
}#outlier function is defined in previous chunck of code.
outlier_check_price = outlierKD2(data_final, Price, rm = FALSE, boxplt = TRUE, qqplt = TRUE)
## Outliers identified: 756
## Proportion (%) of outliers: 8.5
## Mean of the outliers: 14.05
## Mean without removing outliers: 1.1
## Mean if we remove outliers: 0The price values in the dataset, including both typical and extreme values, are valid observations for our analysis. As such, removing these outliers may not be beneficial for our study.
#To check the value ranges
table(data_final$Price)##
## 0 0.99 1 1.04 1.2 1.26 1.29 1.49 1.5 1.59 1.61
## 8903 145 3 1 1 1 1 46 1 1 1
## 1.7 1.75 1.76 1.96 1.97 1.99 2 2.49 2.5 2.56 2.59
## 2 1 1 1 1 73 3 25 1 1 1
## 2.6 2.9 2.95 2.99 3.02 3.04 3.08 3.28 3.49 3.61 3.88
## 1 1 1 124 1 1 1 1 7 1 1
## 3.9 3.95 3.99 4.29 4.49 4.59 4.6 4.77 4.8 4.84 4.85
## 1 1 57 1 9 1 1 1 1 1 1
## 4.99 5 5.49 5.99 6.49 6.99 7.49 7.99 8.49 8.99 9
## 70 1 5 26 5 11 2 7 2 5 1
## 9.99 10 10.99 11.99 12.99 13.99 14 14.99 15.46 15.99 16.99
## 19 2 2 3 4 2 1 9 1 1 2
## 17.99 18.99 19.4 19.9 19.99 24.99 25.99 28.99 29.99 30.99 33.99
## 2 1 1 1 5 3 1 1 5 1 1
## 37.99 39.99 46.99 74.99 79.99 89.99 109.99 154.99 200 299.99 379.99
## 1 2 1 1 1 1 1 1 1 1 1
## 389.99 394.99 399.99 400
## 1 1 12 1As aldready mentioned, there are 8903 free apps (More apps with price as 0).
Visualization for Type Distribution
# Bar Plot for the Type Distribution
ggplot(data_final, aes(x = Type)) +
geom_bar(fill = "pink", color = "black") +
labs(title = "Distribution of App Types (Free vs Paid)", x = "Type", y = "Count") +
theme_minimal()
As it is clear, there are more free apps.
#Display statistics for the Price of apps grouped by their Type
data_final$Type <- as.factor(data_final$Type)
summary_by_type <- data.frame(
Type = levels(data_final$Type),
Min_Price = tapply(data_clean$Price, data_clean$Type, min, na.rm = TRUE),
Max_Price = tapply(data_clean$Price, data_clean$Type, max, na.rm = TRUE),
Mean_Price = tapply(data_clean$Price, data_clean$Type, mean, na.rm = TRUE),
Median_Price = tapply(data_clean$Price, data_clean$Type, median, na.rm = TRUE)
)
print(summary_by_type)## Type Min_Price Max_Price Mean_Price Median_Price
## Free Free 0.00 0 0.00000 0.00
## NaN NaN 0.00 0 0.00000 0.00
## Paid Paid 0.99 400 14.04515 2.99#Scatter plot for price distribution by app type
ggplot(data_final, aes(x = Type, y = Price, fill = Type)) +
geom_boxplot() +
labs(title = "Price Distribution by App Type",
x = "App Type",
y = "Price ($)") +
theme_minimal()
Histogram for price distribution by App Type
ggplot(data_final, aes(x = Price, fill = Type)) +
geom_histogram(binwidth = 60, alpha = 0.7, position = "identity") +
facet_wrap(~ Type) +
labs(title = "Price Distribution by App Type",
x = "Price ($)",
y = "Count") +
theme_minimal()
Upon analyzing the price distribution across different app types, we found that some values in the Type column do not accurately represent the app prices (from above plot). Since we can fully rely on the Price values for our analysis, the Type column is seemed unnecessary.
Hence, Removing the Type column…
Dropping the Type column
#Using subset function
data_final <- subset(data_final, select = -Type)#After removing the Type column and duplicated values
str(data_final)## 'data.frame': 9659 obs. of 10 variables:
## $ App : chr "Photo Editor & Candy Camera & Grid & ScrapBook" "Coloring book moana" "U Launcher Lite – FREE Live Cool Themes, Hide Apps" "Sketch - Draw & Paint" ...
## $ Category : Factor w/ 33 levels "ART_AND_DESIGN",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Rating : num 4.1 3.9 4.7 4.5 4.3 4.4 3.8 4.1 4.4 4.7 ...
## $ Reviews : num 159 967 87510 215644 967 ...
## $ Size : num 19 14 8.7 25 2.8 5.6 19 29 33 3.1 ...
## $ Installs : num 1e+04 5e+05 5e+06 5e+07 1e+05 5e+04 5e+04 1e+06 1e+06 1e+04 ...
## $ Price : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Content.Rating: chr "everyone" "everyone" "everyone" "teen" ...
## $ Last.Updated : Date, format: "2018-01-07" "2018-01-15" ...
## $ Android.Ver : Factor w/ 34 levels "1.0 and up","1.5 and up",..: 16 16 16 19 21 9 16 19 11 16 ...The Type column is successfully removed.
Let’s do bivariate analysis on price and other variables starting from here.
Visualization for Price vs Installs
#Plotting a scatter plot between Price and installs
ggplot(data_final, aes(x=Price, y=log(data_clean$Installs))) +
geom_point(color = 'red', size = 1, alpha = 0.5) +
geom_smooth(method = 'lm', color = 'blue', se = FALSE) +
labs(title = "Price vs Installs", x = "Price (USD)", y = "Number of Installs") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
From the scatter plot, we can see that there are more number of
installations with price value 0.
# Categorize the apps as "Free" or "Paid" based on Price
Price_Category <- ifelse(data_final$Price == 0, "Free", "Paid")
str(data_final$Price)## num [1:9659] 0 0 0 0 0 0 0 0 0 0 ...str(Price_Category)## chr [1:9659] "Free" "Free" "Free" "Free" "Free" "Free" "Free" "Free" ...#str(log(data_clean$Installs))For a better visualization, we are categorizing price values 0 as free apps and plotting abox plot.
# Box plot of Price Category vs. log-transformed Installs
ggplot(data_final, aes(x = Price_Category, y = log(data_clean$Installs))) +
geom_boxplot(fill = "lightblue", color = "darkblue", alpha = 0.6) +
labs(title = "Price Categories vs. Log-Transformed Installs",
x = "Price Category",
y = "Log(Installs)") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) 
“Free” apps tend to have more installs than “Paid” apps. The difference between the means on the log scale is estimated to be between 3.47 and 3.97.
# Categorize the apps as "Free" or "Paid" based on Price
Price_Category <- ifelse(data_final$Price == 0, "Free", "Paid")
str(data_final$Price)## num [1:9659] 0 0 0 0 0 0 0 0 0 0 ...str(Price_Category)## chr [1:9659] "Free" "Free" "Free" "Free" "Free" "Free" "Free" "Free" ...#str(data_final$log(data_clean$Installs))
table(Price_Category)## Price_Category
## Free Paid
## 8903 756# Add Price_Category to data_final
data_duplicate <- data_final
data_duplicate$Price_Category <- ifelse(data_final$Price == 0, "Free", "Paid")
# Create a summarized table for Price_Category and log_Installs
summary_table <- data_duplicate %>%
group_by(Price_Category) %>%
summarise(Average_Log_Installs = mean(log(data_clean$Installs), na.rm = TRUE),
Count = n())
# View the summarized table
kable(summary_table, format = "html", col.names = c("Price Category", "Mean Log(Installs)", "App Count")) %>%
kable_styling(full_width = FALSE, position = "center") | Price Category | Mean Log(Installs) | App Count |
|---|---|---|
| Free | -Inf | 8903 |
| Paid | -Inf | 756 |
Visualization for Price vs Reviews & Rating
# Plot Price vs. Reviews
ggplot(data_final, aes(x=Price, y=Reviews)) +
geom_point(color = 'blue') +
geom_smooth(method = 'lm', color = 'red', se = FALSE) +
labs(title = "Price vs Reviews", x = "Price (USD)", y = "Number of Reviews") +
theme_minimal() +
theme(
panel.background = element_rect(fill = "white"), # Set panel background to white
plot.background = element_rect(fill = "white"), # Set plot background to white
axis.text.x = element_text(angle = 45, hjust = 1)
)
# Plot Price vs. Rating
ggplot(data_final, aes(x=Price, y=Rating)) +
geom_point(color = 'green') +
geom_smooth(method = 'lm', color = 'red', se = FALSE) +
labs(title = "Price vs Rating", x = "Price (USD)", y = "Rating") +
theme_minimal() +
theme(
panel.background = element_rect(fill = "white"), # Set panel background to white
plot.background = element_rect(fill = "white"), # Set plot background to white
axis.text.x = element_text(angle = 45, hjust = 1)
)
Price vs Reviews with installation: Cheaper products tend to have more reviews, indicating higher popularity or more frequent purchases. In contrast, expensive products tend to have fewer reviews, possibly because fewer people buy higher-priced items.
Price vs Ratings with installation: Price does not strongly affect the average rating, but there is a slight trend where lower-priced products have more variation in ratings, while higher-priced products tend to receive more consistent ratings around 4. May be higher price apps are meeting the customer expectations.
Visualization for Price vs Reviews vs Installs
# Scatter plot of Price vs. Ratings with log_Installs as color
ggplot(data_final, aes(x = Price, y = Rating,color = log(data_clean$Installs))) +
geom_point(alpha = 0.6) +
scale_color_gradient(low = "blue", high = "red") +
labs(title = "Price vs. Ratings with Installs as Color by Price",
x = "Price",
y = "Rating",
color = "log(Installs)") +
theme_minimal()
# Scatter plot of Price vs. Reviews with log_Installs as color
ggplot(data_final, aes(x = Price, y = Reviews,color = log(data_clean$Installs))) +
geom_point(alpha = 0.6) +
scale_color_gradient(low = "darkgreen", high = "yellow") +
labs(title = "Price vs. reviewss with Installs as Color by Price",
x = "Price",
y = "Reviews",
color = "log(Installs)") +
theme_minimal()
Concluding: Apps with lower prices, have more ratings and installs while apps priced higher tend to have fewer installs and more scattered ratings. Similarly, for reviews.
Visualization for Price vs Size
# Plot Price vs Size
ggplot(data_final, aes(x=Price, y=Size)) +
geom_point(color = 'red') +
geom_smooth(method = 'lm', color = 'blue', se = FALSE) +
labs(title = "Price vs Size", x = "Price (USD)", y = "App Size (MB)") +
theme_minimal() 
#### Visualization for paid apps vs category
# Filter only paid apps
paid_apps <- data_duplicate %>% filter(Price_Category == "Paid")
ggplot(paid_apps, aes(x = Category)) +
geom_bar(fill = "skyblue", color = "black") +
labs(title = "Distribution of Categories for Paid Apps",
x = "App Category",
y = "Count of Paid Apps") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Few Categories have a high count of paid apps, such as “Family,” “Health
and Fitness,” and “Personalization” which tells us that users may be
more willing to pay for apps in these categories, possibly due to the
quality or utility they offer.
Categories like “Dating,” “Weather,” and “Education” have very few paid apps, indicating lower availability or demand for paid versions in these areas.
Visulization for Distribution of Installs
# Create a copy of data_final for factor-level modifications
data_clean1_factor <- data_final
# Define breakpoints and labels for the Installs factor
breaks <- c(0, 500, 1000, 2500, 5000, 10000, 25000, 50000, 100000, 300000, 1000000, 5000000,10000000,Inf)
labels <- c("0+","500+", "1K+", "2.5K+", "5K+", "10K+",
"25K+", "50K+", "100K+", "300K+", "1M+", "5M+","Above 10M+" )
# Convert Installs into a factor with the defined levels
data_clean1_factor$Installs <- cut(data_final$Installs, breaks = breaks, right = FALSE, labels = labels)
# Create a bar plot with the ordered factor
ggplot(data_clean1_factor, aes(x = Installs)) +
geom_bar() +
xlab("Installs") +
ylab("Count") +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
ggtitle("Distribution of App Installs")
This plot shows a common trend where many apps have limited user engagement, while a few high-performing apps achieve very high install counts, indicating a polarized distribution of app popularity.
Visualization for Rating Distribution
boxplot(data_final$Rating,ylab = "Rating", xlab = "Count",col = "Blue")
hist(data_clean$Rating, main="Histogram of Apps Rating after cleaning", xlab="Rating (count)", col = 'blue', breaks = 100 )
qqnorm(data_clean$Rating)
qqline(data_clean$Rating, col = "red")
Here, it could be seen the plots are much clearer but still skewed due to other outliers from 1-3 rating but as these may be the reason from which we could find why the apps are low rated hencecannot be removed from our dataset.
Visualization for Reviews
boxplot(data_final$Reviews,ylab = "Reviews", xlab = "Count",col = 'Blue')
hist(data_final$Reviews, main="Histogram of Apps Reviews", xlab="Reviews (count)", col = 'blue', breaks = 100 )
ggplot(data_final, aes(x = log(Reviews))) +
geom_histogram(binwidth = 0.1, fill = "blue", color = "black") +
labs(title = "Log-Transformed Histogram of Ratings", x = "Log(Rating)", y = "Count")
qqnorm(data_final$Reviews)
qqline(data_final$Reviews, col = "red")
Similar to the case of ratings the plots are skewed due to the outliers. Hence, we can use the log plot of reviews for the visualisation which is normalised version of Reviews. As they are skewed, they donot follow normal distribution.
Review frequency table
xkablesummary(data_final)| App | Category | Rating | Reviews | Size | Installs | Price | Content.Rating | Last.Updated | Android.Ver | |
|---|---|---|---|---|---|---|---|---|---|---|
| Min | Length:9659 | FAMILY :1832 | Min. :1.000 | Min. : 0 | Min. : 0.0085 | Min. :0.000e+00 | Min. : 0.000 | Length:9659 | Min. :2010-05-21 | 4.1 and up :2202 |
| Q1 | Class :character | GAME : 959 | 1st Qu.:4.000 | 1st Qu.: 25 | 1st Qu.: 5.3000 | 1st Qu.:1.000e+03 | 1st Qu.: 0.000 | Class :character | 1st Qu.:2017-08-05 | 4.0.3 and up :1395 |
| Median | Mode :character | TOOLS : 827 | Median :4.200 | Median : 967 | Median : 13.1000 | Median :1.000e+05 | Median : 0.000 | Mode :character | Median :2018-05-04 | 4.0 and up :1285 |
| Mean | NA | BUSINESS : 420 | Mean :4.173 | Mean : 216593 | Mean : 20.1512 | Mean :7.778e+06 | Mean : 1.099 | NA | Mean :2017-10-30 | Varies with device: 990 |
| Q3 | NA | MEDICAL : 395 | 3rd Qu.:4.500 | 3rd Qu.: 29401 | 3rd Qu.: 27.0000 | 3rd Qu.:1.000e+06 | 3rd Qu.: 0.000 | NA | 3rd Qu.:2018-07-17 | 4.4 and up : 818 |
| Max | NA | PERSONALIZATION: 376 | Max. :5.000 | Max. :78158306 | Max. :100.0000 | Max. :1.000e+09 | Max. :400.000 | NA | Max. :2018-08-08 | 2.3 and up : 616 |
| NA | NA | (Other) :4850 | NA | NA | NA | NA | NA | NA | NA | (Other) :2353 |
outlierKD2(data_final, Reviews)## Outliers identified: 1656
## Proportion (%) of outliers: 20.7
## Mean of the outliers: 1228141
## Mean without removing outliers: 216592.6
## Mean if we remove outliers: 7280.61
To check which are outliers lets make sections of data that is create bins to check which bins have maximum data, this would help us see how reviews are distributed.
Binned reviews
Binning into equal count in each bin to check averge rating for each bin
# Define the new custom breaks for bins
# Ensure there are no NA values
# Define new breaks for more even intervals
breaks <- c(0, 100, 500, 1000, 2500, 5000, 10000, 25000,50000,100000, 300000,1000000,Inf)
# Create a categorical variable based on the new breaks
Review_Category <- cut(data_final$Reviews, breaks = breaks, right = FALSE,
labels = c("0+","100+", "500+", "1K+",
"2.5K+", "5K+", "10K+","25K+",
"50K+", "100K+","300K+","1M+"))
# Count the number of values in each bin
bin_counts <- as.data.frame(table(Review_Category))
# Rename the columns for clarity
colnames(bin_counts) <- c("Review_Category", "Count")
# Print the counts
print(bin_counts)## Review_Category Count
## 1 0+ 3327
## 2 100+ 1065
## 3 500+ 462
## 4 1K+ 586
## 5 2.5K+ 475
## 6 5K+ 474
## 7 10K+ 719
## 8 25K+ 606
## 9 50K+ 498
## 10 100K+ 647
## 11 300K+ 451
## 12 1M+ 349# Create a line plot of the binned counts
ggplot(bin_counts, aes(x = Review_Category, y = Count, group = 1)) +
geom_line(color = "blue", size = 1) +
geom_point(color = "blue", size = 3) +
labs(title = "Count of Reviews by Review Category",
x = "Review Category",
y = "Count of Reviews") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) # Rotate x-axis labels for readability
Hence, high reviews can be observed in less apps and less reviews can be observed in more apps which is expected.
Boxplots for Rating vs Reviews
boxplot( data_final$Rating~ Review_Category, data = data_clean,
main = "Boxplot of Review Counts by Review Category",
xlab = "Review Category",
ylab = "Review Rating",
las = 2, # Rotate the x-axis labels for readability
col = "lightblue") # Optional: Set color for the boxplots
In this we could observe that, as reviews increase the median of rating increased and the values clustered around higher ratings which could show that high reviews, could mean a better rated app.
Mean value of Ratings for each Review bins
# Calculate the mean Rating for each Review_Category
mean_ratings <- tapply(data_final$Rating, Review_Category, mean, na.rm = TRUE)
# Convert the result to a data frame for better readability
mean_ratings_df <- data.frame(Review_Category = names(mean_ratings), Mean_Rating = as.numeric(mean_ratings))
# Print the mean ratings for each review bin
print(mean_ratings_df)## Review_Category Mean_Rating
## 1 0+ 4.126221
## 2 100+ 4.029538
## 3 500+ 4.063188
## 4 1K+ 4.107030
## 5 2.5K+ 4.129572
## 6 5K+ 4.191139
## 7 10K+ 4.221836
## 8 25K+ 4.231848
## 9 50K+ 4.293775
## 10 100K+ 4.329830
## 11 300K+ 4.375610
## 12 1M+ 4.426361# Define correct order of Review_Category as a factor
mean_ratings_df$Review_Category <- factor(mean_ratings_df$Review_Category,
levels = c("0+","100+", "500+", "1K+",
"2.5K+", "5K+", "10K+","25K+",
"50K+", "100K+", "300K+", "1M+"))
# Plot the mean ratings for each review bin in the correct order
ggplot(mean_ratings_df, aes(x = Review_Category, y = Mean_Rating)) +
geom_bar(stat = "identity", fill = "steelblue") + # Use bar plot
labs(title = "Mean Rating by Review Category",
x = "Review Category",
y = "Mean Rating") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) # Rotate x-axis labels for readability
As we can see, the mean rating increases as the reviews increase.
Histogram for Reviews and Rating
# Create a new data frame for plotting
plot_data <- data.frame(Rating = data_final$Rating, Review_Category = Review_Category)
# Create a histogram of Ratings, faceted by Review_Category
ggplot(plot_data, aes(x = Rating)) +
geom_histogram(bins = 30, fill = "blue", alpha = 0.7) +
facet_wrap(~ Review_Category, labeller = label_wrap_gen()) + # Facet by Review_Category
theme_minimal() +
labs(title = "Histograms of Ratings by Review Category", x = "Rating", y = "Frequency")
This is another representation of ratings vs reviews.
Visualization for Installs vs Size
ggplot(data_clean, aes(x = Size, y = log(Installs))) +
geom_hex(bins = 30) +
scale_fill_viridis_c() + # Adds color gradient
labs(title = "Plot of App Size vs. Installs (Log Scale)",
x = "Size (MB)",
y = "Installs (Log Scale)") +
theme_minimal()
This analysis shows that apps with medium file sizes (around 20-50 MB) tend to be more popular and get downloaded more often. On the other hand, larger apps (over 75 MB) don’t get downloaded as much, possibly because they take up more space on devices or are slower to download.
Visualization for Reviews vs Installs
# Scatter plot for Installs vs Reviews
ggplot(data_clean1_factor, aes(x = Review_Category, y = Installs)) +
geom_point(color = "blue", alpha = 0.5) +
geom_smooth(method = "lm", color = "red", se = FALSE) + # Add a regression line
labs(title = "Scatter Plot of Installs vs Reviews",
x = "Number of Reviews",
y = "Number of Installs") +
theme_minimal()
This scatter plot shows that as apps get more downloads, they tend to get more reviews from users. Most apps fall in the lower range of downloads (like 0 to 50K installs), meaning they get a moderate number of reviews. Popular apps with over a million downloads often have thousands of reviews, showing strong user engagement. However, very few apps reach extremely high review counts (like 100K+ reviews), indicating that only a few apps become extremely popular. In short, the more installs an app has, the more likely it is to gather user feedback in the form of reviews.
Visualisation of Mean for different Install Categories
# Calculate the mean Rating for each Review_Category
mean_ratings <- tapply(data_final$Rating, data_clean1_factor$Installs, mean, na.rm = TRUE)
# Convert the result to a data frame for better readability
mean_ratings_df <- data.frame(Installs = names(mean_ratings), Mean_Rating = as.numeric(mean_ratings))
# Print the mean ratings for each review bin
print(mean_ratings_df)## Installs Mean_Rating
## 1 0+ 4.247797
## 2 500+ 4.176062
## 3 1K+ 4.086812
## 4 2.5K+ NA
## 5 5K+ 4.035362
## 6 10K+ 4.041438
## 7 25K+ NA
## 8 50K+ 4.048356
## 9 100K+ 4.117373
## 10 300K+ 4.168462
## 11 1M+ 4.216335
## 12 5M+ 4.227677
## 13 Above 10M+ 4.316338mean_ratings_df$Installs = factor(mean_ratings_df$Installs, levels = c(0,1,5,10,50,100,500,1000,5000,10000,50000,100000,500000,1000000,5000000,10000000,50000000,100000000,500000000,1000000000))
# Plot the mean ratings for each review bin in the correct order
ggplot(mean_ratings_df, aes(x = Installs, y = Mean_Rating)) +
geom_bar(stat = "identity", fill = "steelblue") + # Use bar plot
labs(title = "Mean Rating by Install Category",
x = "Installs Category",
y = "Mean Rating") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) # Rotate x-axis labels for readability
Observing the flucuation of Rating for different Installs it could be
seen that there is no constant increase or deacrease trend seen for
Installs and rating, which could be expected as more Rating doesnot
necessarily mean more Installs. But high Installs and high Rating could
be seen as good app.
Visualization for Rating vs Installs
# Scatter plot of log-transformed Installs vs. Rating
ggplot(data_final, aes(x = log(Installs) , y = Rating)) +
geom_point(color = "blue", alpha = 0.6) +
geom_smooth(method = "lm", color = "red", se = FALSE) + # Add a regression line
labs(title = "Log-Transformed Installs vs. Rating",
x = "Rating",
y = "Installs") +
theme_minimal()
The scatter plot shows a weak positive correlation between app installs and ratings, as indicated by the nearly flat red trend line. Data points are clustered at specific rating levels, suggesting many apps share similar ratings but vary significantly in install counts. The x-axis range, extending to 20, is unusual for typical rating scales (e.g., 1-5), possibly indicating data irregularities or transformations. The y-axis, log-transformed, reveals a wide distribution in install counts. Overall, ratings seem to have minimal impact on installs, and the data’s clustering suggests further examination of the rating scale may be necessary.
Visualization for Rating vs Installs by Category
This scatter plot illustrates the relationship between log-transformed installs and ratings across app categories. Each category has distinct symbols and colors, showing varying distributions in ratings and installs. Higher-rated apps (around 4-5) are more densely populated across several categories, while lower-rated apps are sparse. Some categories, such as “LIFESTYLE” and “FINANCE,” have a broad range of installs and ratings, while others are tightly clustered. The spread of installs varies widely, especially among apps with similar ratings, suggesting that category influences install counts significantly. Overall, higher ratings correlate with greater install variability across categories.
Visualization for Category Distribution
category_counts <- table(data_final$Category)
# Convert to data frame for plotting
category_counts_df <- as.data.frame(category_counts)
colnames(category_counts_df) <- c("Category", "Frequency")
ggplot(category_counts_df, aes(x = reorder(Category, Frequency), y = Frequency)) +
geom_bar(stat = "identity", fill = "#1f3374") +
geom_text(aes(label = Frequency), vjust = 0.5, hjust=1, size=2.5, color='#f8c220') +
coord_flip() +
labs(title = "Distribution of Categories", x = "Category", y = "Frequency") +
theme_minimal() +
theme(
plot.background = element_rect(fill = "#efefef", color = NA),
panel.background = element_rect(fill = "#efefef", color = NA),
axis.text.y = element_text(size = 5.5)
)
AS it can be seen from the graph above, most of the apps in the dataset belong to the Family and Game, tools category, and Beauty,comics have the least number of apps.
Visualization for Category vs. Installs
Below is a boxplot show the distribution of number of installs for each category order by mean from highest to lowest.
ggplot(data_clean, aes(x = reorder(Category, log(data_final$Installs), FUN = mean), y = log(data_clean$Installs))) +
geom_boxplot(outlier.color = "#f05555", outlier.shape = 1, color='#1f3374', fill="#efefef") + # Red outliers for emphasis
coord_flip() + # Flip for better readability
scale_y_log10() +
theme_minimal() +
labs(title = "Distribution of Installs by Category",
x = "Category",
y = "Number of Installs (Log Scale)") +
theme(
plot.background = element_rect(fill = "#efefef", color = NA),
panel.background = element_rect(fill = "#efefef", color = NA),
axis.text.y = element_text(size = 5.5)
)
It can be seen from the graph that, on average, Entertainment apps
receive the highest number of installations, followed by Education,
Game, Photography, and Weather apps. In contrast, Art & Design apps
have the fewest installations.
Visualization for Category vs. App Size
#convert_size <- function(size) {
# size <- gsub(",", "", size) # Remove commas
# size <- tolower(size) # Make lowercase for consistency
# Handle "varies with device" by assigning NA
# if (size == "varies with device") return(NA)
# Convert "k" to MB (1 MB = 1000 KB)
# if (grepl("k", size)) return(as.numeric(gsub("k", "", size)) / 1000)
# Convert "M" to numeric MB
# if (grepl("m", size)) return(as.numeric(gsub("m", "", size)))
# Handle numeric values directly (e.g., "1000+")
# if (grepl("\\d+\\+", size)) return(as.numeric(gsub("\\+", "", size)) / 1000)
# Default case: return as numeric if possible
#return(as.numeric(size))
#}Below is the figure showing the distribution of app sizes in each category.
#df_clean <- data_clean %>%
# mutate(Size = sapply(Size, convert_size)) %>%
# filter(!is.na(Size))
# Plot the histogram with faceting by category
ggplot(data_clean, aes(x = Size)) +
geom_histogram(binwidth = 5, fill = "#304ba6", color = "black") +
facet_wrap(~ Category, scales = "free_y") +
theme_minimal() +
labs(
title = "Distribution of App Sizes by Category",
x = "Size (MB)",
y = "Count"
) +
theme(
strip.text = element_text(size = 5),
axis.text.x = element_text(size = 7, angle = 45, hjust = 1)
)
ggplot(data_clean, aes(x = reorder(Category, Size, FUN = median), y = Size)) +
geom_boxplot(outlier.color = "#f05555", outlier.shape = 1) +
coord_flip() +
theme_minimal() +
labs(
title = "Boxplot of App Sizes by Category (Ordered by Median)",
x = "Category",
y = "Size (MB)"
) +
theme(
strip.text = element_text(size = 8),
axis.text.x = element_text(size = 7, angle = 45, hjust = 1)
)
As it can be seen from the two figures above, most categories exhibit right-skewed app sizes, with the majority being under 50MB. However, the Game category stands out with a significantly larger median app size compared to other categories.
Visualization for Category vs. Reviews
Below is the graph displaying the distribution of reviews left by users for each category.
df_aggregated <- data_final %>%
group_by(Category) %>%
summarise(Total_Reviews = sum(Reviews, na.rm = TRUE))
#df_aggregated# Plot the total reviews by category using a bar chart
ggplot(df_aggregated, aes(x = reorder(Category, -Total_Reviews), y = log10(Total_Reviews))) +
geom_bar(stat = "identity", fill = "#1f3374") +
labs(
title = "Log-Scaled Total Reviews by Category",
x = "Category",
y = "Log10(Total Number of Reviews)"
) +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
AS it can be seen that game apps have most reviews while events apps
have the least reviews.
Histogram for Category vs. Rating
Below is the figure demonstrating the distribution of number of rating for each category.
ggplot(data_final, aes(x = Rating)) +
geom_histogram(binwidth = 0.5, fill = "#1f3374", color='#efefef') +
facet_wrap(~ Category, scales = "free_y") + # Facet by Category with independent y-axis
scale_x_continuous(limits = c(1, 5), breaks = seq(1, 5, by = 0.5)) + # Restrict x-axis to 1-5
theme_minimal() +
labs(
title = "Distribution of Ratings by Category",
x = "Rating",
y = "Count"
) +
theme(
strip.text = element_text(size = 5), # Adjust facet label size
axis.text.x = element_text(size = 5, angle = 45, hjust = 1), # Rotate x-axis labels
plot.title = element_text(hjust = 0.5) # Center the plot title
)
As illustrated in the graph above, all categories have app ratings that
range between 4.0 and 5.0.
Visualization for Android Version
Below is the figure showing the distribution of Android versions.
extract_version <- function(version) {
version <- tolower(version) # Make lowercase for consistency
# Handle "Varies with device" and "NaN"
if (version == "varies with device" || version == "nan") return(NA)
# Extract the first version in case of ranges (e.g., "4.1 - 7.1.1" -> "4.1")
first_version <- strsplit(version, "[- ]")[[1]][1]
# Remove "and up" if present (e.g., "4.0 and up" -> "4.0")
first_version <- gsub("and up", "", first_version)
return(as.numeric(first_version)) # Convert to numeric
}df_clean <- data_final %>%
mutate(Android_Ver = sapply(Android.Ver, extract_version)) %>%
filter(!is.na(Android_Ver)) # Remove rows with NA in Android_Ver
android_installs <- data_final %>%
group_by(Android.Ver) %>%
summarize(Total_Installs = sum(Installs, na.rm = TRUE))ggplot(df_clean, aes(x = Android_Ver)) +
geom_histogram(binwidth = 0.5, fill = "#1f3374", color='#efefef') +
scale_x_continuous(breaks = seq(1, 8, by = 1.0)) + # Set x-axis ticks from 1.0 to 8.0
theme_minimal() +
labs(
title = "Distribution of Android Versions",
x = "Android Version",
y = "Count"
) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
As it can be seen that, the minimum required Android Version for most
apps is 4.0 and up.
extract_version <- function(version) {
version <- tolower(version) # Make lowercase for consistency
# Handle "Varies with device" and "NaN"
if (version == "varies with device" || version == "nan") return(NA)
# Extract the first version in case of ranges (e.g., "4.1 - 7.1.1" -> "4.1")
first_version <- strsplit(version, "[- ]")[[1]][1]
# Remove "and up" if present (e.g., "4.0 and up" -> "4.0")
first_version <- gsub("and up", "", first_version)
return(as.numeric(first_version)) # Convert to numeric
}Bar plot for Android Version vs. Installs
Below is the graph showing the number of installs for each minimum required Android Version.
ggplot(data_final, aes(x = reorder(Android.Ver, Installs), y = Installs)) +
geom_bar(stat = "identity", fill = "#1f3374") +
coord_flip() + # Flip coordinates for better readability
scale_y_continuous(labels = scales::comma) + # Format y-axis with commas
theme_minimal() +
labs(
title = "Total Installs by Android Version",
x = "Android Version",
y = "Total Installs"
) +
theme(
axis.text.y = element_text(size = 8), # Adjust y-axis text size
plot.title = element_text(hjust = 0.5) # Center the plot title
)
It can be seen that the highest number of installation is when there is different requirements of the versions for the app to run.
Boxplot for Android Version vs. Reviews
Below is the distribution of reviews for each minimum required Android Version.
df_clean <- data_final %>%
filter(!is.na(Android.Ver) & !is.na(Reviews)) %>%
mutate(Scaled_Reviews = log10(Reviews + 1))ggplot(df_clean, aes(x = reorder(Android.Ver, Scaled_Reviews, FUN = median), y = Scaled_Reviews)) +
geom_boxplot(outlier.color = "#f05555", outlier.shape = 1) + # Boxplot with red outliers
coord_flip() + # Flip coordinates for better readability
theme_minimal() +
labs(
title = "Distribution of Scaled Reviews by Android Version",
x = "Android Version",
y = "Scaled Reviews (Log10)"
) +
theme(
axis.text.y = element_text(size = 8), # Adjust y-axis text size
plot.title = element_text(hjust = 0.5) # Center the plot title
)
It can be seen that the version from 4.1 to 7.1.1 have the highest number of reviews, whiel version from 5.0 to 7.1.1 have the least number of reviews.
Histogram for Android Version vs. Rating
Below is the plot showing the number of ratings for each Android Version.
ggplot(df_clean, aes(x = Rating, fill = Android.Ver)) +
geom_histogram(binwidth = 0.5, position = "stack", color = "black", alpha = 0.7) +
scale_x_continuous(breaks = seq(1, 5, by = 0.5)) + # Set x-axis breaks
theme_minimal() +
labs(
title = "Histogram of Ratings by Android Version",
x = "Rating",
y = "Count"
) +
theme(
axis.text.x = element_text(size = 8),
axis.text.y = element_text(size = 8),
plot.title = element_text(hjust = 0.5) # Center the plot title
)
It can be seen that most Android Version have ratings range between 4.0
and 5.0.
Distribution for Content.Rating
# Clean and prepare the Last Updated and Content column
data_final <- data_final %>%
mutate(
Content.Rating = as.factor(Content.Rating)
)
#Content Rating Distribution
content_rating_dist <- table(data_final$Content.Rating)
print("Content Rating Distribution:")## [1] "Content Rating Distribution:"print(content_rating_dist)##
## adults only 18+ everyone everyone 10+ mature 17+ teen
## 3 7903 322 393 1036
## unrated
## 2Visualization for Content Rating
# Bar plot for Content Rating
ggplot(data_final, aes(x = Content.Rating)) +
geom_bar(fill = "skyblue") +
geom_text(stat = "count", aes(label = ..count..), vjust = -0.5) +
labs(title = "Distribution of App Content Ratings",
x = "Content Rating",
y = "Number of Apps") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Everyone is the most dominant Category with 81.82% of all apps and
Adults 18+ being most least significant category with about 0.03% of
overall app population
# Last Updated Analysis
# Create summary of updates by month and year
updates_by_month <- data_final %>%
mutate(
update_month = format(Last.Updated, "%Y-%m"),
update_year = year(Last.Updated)
) %>%
group_by(update_month) %>%
summarize(count = n()) %>%
arrange(update_month)# Plot updates over time
#ggplot(updates_by_month, aes(x = as.Date(paste0(update_month, "-01")), y = count)) +
#geom_line(color = "blue") +
#geom_point(color = "red") +
#labs(title = "Number of App Updates Over Time",
# x = "Date",
# y = "Number of Updates") +
#theme_minimal() +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))The number of updates have drastically increased from the end of 2017
# Content Rating and Update Frequency Relationship
update_frequency_by_rating <- data_final %>%
group_by(Content.Rating) %>%
summarize(
avg_last_update = mean(Last.Updated),
median_last_update = median(Last.Updated),
n_apps = n()
)
print("\nUpdate Frequency by Content Rating:")## [1] "\nUpdate Frequency by Content Rating:"print(update_frequency_by_rating)## # A tibble: 6 × 4
## Content.Rating avg_last_update median_last_update n_apps
## <fct> <date> <date> <int>
## 1 adults only 18+ 2018-07-20 2018-07-24 3
## 2 everyone 2017-10-20 2018-04-20 7903
## 3 everyone 10+ 2017-11-24 2018-06-06 322
## 4 mature 17+ 2018-02-18 2018-07-09 393
## 5 teen 2017-12-03 2018-06-05 1036
## 6 unrated 2013-10-25 2013-10-25 2# Content Rating Basic Analysis
#print("Basic Content Rating Analysis:")
#content_rating_counts <- table(data_final$Content.Rating)
#print(content_rating_counts)
# Basic bar plot for Content Rating
#ggplot(data_final, aes(x = Content.Rating)) +
# geom_bar(fill = "skyblue") +
# geom_text(stat = "count", aes(label = ..count..), vjust = -0.5) +
# labs(title = "Distribution of App Content Ratings",
# x = "Content Rating",
# y = "Number of Apps") +
# theme_minimal() +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))
#
# # Calculate percentages
# content_rating_percentages <- prop.table(content_rating_counts) * 100
# print("\nContent Rating Percentages:")
# print(round(content_rating_percentages, 2))
#
# # 1.2 Last Updated Basic Analysis
# data_final$Last.Updated <- as.Date(data_final$Last.Updated, format = "%B %d, %Y")
#
# print("\nLast Updated Summary Statistics:")
# summary(data_final$Last.Updated)# Create a duplicate dataframe for time-based analysis, use data_time_analysis
data_time_analysis <- data_final %>%
mutate(Last.Updated = as.Date(Last.Updated, format = "%B %d, %Y"))
# Calculate max(Last.Updated)
max_last_updated <- max(data_time_analysis$Last.Updated, na.rm = TRUE)
# Add columns for update year, month, quarter, and days since last update
data_time_analysis <- data_time_analysis %>%
mutate(
update_year = year(Last.Updated),
update_month = month(Last.Updated),
update_quarter = quarter(Last.Updated),
days_since_update = as.numeric(difftime(max_last_updated, Last.Updated, units = "days"))
)
# Monthly update pattern
monthly_updates <- data_time_analysis %>%
group_by(update_year, update_month) %>%
summarize(count = n()) %>%
mutate(date = as.Date(paste(update_year, update_month, "01", sep = "-")))
# Plotting monthly update pattern
ggplot(monthly_updates, aes(x = date, y = count)) +
geom_line(color = "blue") +
geom_point() +
labs(title = "App Updates Over Time",
x = "Date",
y = "Number of Updates") +
theme_minimal()
# Content Rating Distribution by Update Quarter
ggplot(data_time_analysis, aes(x = factor(update_quarter), fill = Content.Rating)) +
geom_bar(position = "dodge") +
labs(title = "Content Rating Distribution by Quarter",
x = "Quarter",
y = "Count") +
theme_minimal()
# Update Frequency Analysis by Content Rating
update_patterns <- data_time_analysis %>%
group_by(Content.Rating) %>%
summarize(
avg_days_since_update = mean(days_since_update),
median_days_since_update = median(days_since_update),
sd_days_since_update = sd(days_since_update),
n_apps = n(),
cv = sd(days_since_update) / mean(days_since_update) * 100 # Coefficient of Variation
) %>%
arrange(avg_days_since_update)
print("\nUpdate Patterns by Content Rating:")## [1] "\nUpdate Patterns by Content Rating:"print(update_patterns)## # A tibble: 6 × 6
## Content.Rating avg_days_since_update median_days_since_update
## <fct> <dbl> <dbl>
## 1 adults only 18+ 18.3 15
## 2 mature 17+ 171. 30
## 3 teen 248. 64
## 4 everyone 10+ 257. 63
## 5 everyone 292. 110
## 6 unrated 1748. 1748.
## # ℹ 3 more variables: sd_days_since_update <dbl>, n_apps <int>, cv <dbl># Advanced Visualization - Heatmap of Updates
update_heatmap_data <- data_time_analysis %>%
group_by(update_month, Content.Rating) %>%
summarize(count = n()) %>%
spread(Content.Rating, count)
# Convert to matrix for heatmap
update_matrix <- as.matrix(update_heatmap_data[,-1])
rownames(update_matrix) <- month.abb[update_heatmap_data$update_month]
# Create heatmap
heatmap(update_matrix,
Colv = NA,
Rowv = NA,
scale = "column",
col = colorRampPalette(c("white", "steelblue"))(50),
main = "Update Pattern Heatmap by Content Rating",
xlab = "Content Rating",
ylab = "Month")
# 3.4 Time Series Decomposition
# Focus on Everyone category as an example
#everyone_ts <- monthly_updates %>%
# filter(count > 0) %>%
# select(count) %>%
# ts(frequency = 12)
#decomposed <- decompose(everyone_ts)
#plot(decomposed)
# Update Velocity Analysis
update_velocity <- data_time_analysis %>%
group_by(Content.Rating) %>%
summarize(
update_velocity = n() / n_distinct(update_month),
total_apps = n()
) %>%
arrange(desc(update_velocity))
print("\nUpdate Velocity by Content Rating:")## [1] "\nUpdate Velocity by Content Rating:"print(update_velocity)## # A tibble: 6 × 3
## Content.Rating update_velocity total_apps
## <fct> <dbl> <int>
## 1 everyone 659. 7903
## 2 teen 86.3 1036
## 3 mature 17+ 32.8 393
## 4 everyone 10+ 26.8 322
## 5 adults only 18+ 1.5 3
## 6 unrated 1 2Observation for Update Frequency Velocity Analysis:
This column represents the average number of updates per app for each content rating category. It reflects how frequently apps in each category receive updates.
# 1. Update Cycle Analysis - use data_update_time_analysis
data_update_time_analysis <- data_time_analysis %>%
mutate(
Last.Updated = as.Date(Last.Updated, format = "%B %d, %Y"),
day_of_week = wday(Last.Updated, label = TRUE),
week_of_year = week(Last.Updated),
month_of_year = month(Last.Updated, label = TRUE),
season = case_when(
month_of_year %in% c("Dec", "Jan", "Feb") ~ "Winter",
month_of_year %in% c("Mar", "Apr", "May") ~ "Spring",
month_of_year %in% c("Jun", "Jul", "Aug") ~ "Summer",
TRUE ~ "Fall"
)
)
# Day of Week Update Pattern by Content Rating
dow_pattern <- data_update_time_analysis %>%
group_by(Content.Rating, day_of_week) %>%
summarise(count = n()) %>%
group_by(Content.Rating) %>%
mutate(percentage = count/sum(count) * 100)
ggplot(dow_pattern, aes(x = day_of_week, y = percentage, fill = Content.Rating)) +
geom_bar(stat = "identity", position = "dodge") +
facet_wrap(~Content.Rating) +
labs(title = "Update Day Preferences by Content Rating",
x = "Day of Week",
y = "Percentage of Updates") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
# 2. Update Interval Analysis
update_intervals <- data_update_time_analysis %>%
group_by(Content.Rating) %>%
arrange(Last.Updated) %>%
mutate(days_between_updates = as.numeric(Last.Updated - lag(Last.Updated))) %>%
summarise(
mean_interval = mean(days_between_updates, na.rm = TRUE),
median_interval = median(days_between_updates, na.rm = TRUE),
std_dev = sd(days_between_updates, na.rm = TRUE),
cv = std_dev / mean_interval * 100 # Coefficient of Variation
)
print("Update Interval Analysis:")## [1] "Update Interval Analysis:"print(update_intervals)## # A tibble: 6 × 5
## Content.Rating mean_interval median_interval std_dev cv
## <fct> <dbl> <dbl> <dbl> <dbl>
## 1 adults only 18+ 15 15 7.07 47.1
## 2 everyone 0.380 0 3.53 929.
## 3 everyone 10+ 8.33 1 46.5 557.
## 4 mature 17+ 5.48 0 21.5 392.
## 5 teen 2.36 0 14.7 622.
## 6 unrated 1213 1213 NA NA# 3. Seasonal Update Intensity
seasonal_intensity <- data_update_time_analysis %>%
group_by(Content.Rating, season) %>%
summarise(
update_count = n(),
update_intensity = n() / n_distinct(Last.Updated)
) %>%
arrange(Content.Rating, desc(update_intensity))
# Visualization of seasonal patterns
ggplot(seasonal_intensity, aes(x = season, y = update_intensity, fill = Content.Rating)) +
geom_bar(stat = "identity", position = "dodge") +
labs(title = "Seasonal Update Intensity by Content Rating",
x = "Season",
y = "Update Intensity") +
theme_minimal()
# 4. Update Clustering Analysis
#update_features <- data_final %>%
# group_by(Content.Rating) %>%
# summarise(
# mean_week = mean(week_of_year),
# std_week = sd(week_of_year),
# update_frequency = n(),
# weekend_ratio = sum(day_of_week %in% c("Sat", "Sun")) / n()
# )
# Normalize the features
#update_features_norm <- scale(update_features[,-1])
#rownames(update_features_norm) <- update_features$Content.Rating
# Perform hierarchical clustering
#update_clusters <- hclust(dist(update_features_norm))
#plot(update_clusters, main = "Hierarchical Clustering of Content Ratings by Update Patterns")# 6. Update Consistency Score
#onsistency_score <- data_final %>%
# group_by(Content.Rating) %>%
# summarise(
# total_updates = n(),
# unique_days = n_distinct(Last.Updated),
# consistency_score = (total_updates / unique_days) *
# (1 - sd(as.numeric(day_of_week)) / 7) # Normalized consistency metric
# ) %>%
# arrange(desc(consistency_score))
#print("\nUpdate Consistency Scores:")
#print(consistency_score)# Convert Last.Updated to numeric (days since reference date) if not already done
# reference_date <- min(data_final$Last.Updated, na.rm = TRUE) # Reference date
# data_final$Days.Since.Update <- as.numeric(data_final$Last.Updated - reference_date)
#
# # Perform the Kolmogorov-Smirnov test on the numeric 'Days.Since.Update' values
# content_ratings <- unique(data_final$Content.Rating)
# ks_results <- data.frame(
# rating1 = character(),
# rating2 = character(),
# p_value = numeric()
# )
#
# for (i in 1:(length(content_ratings)-1)) {
# for (j in (i+1):length(content_ratings)) {
# # Extract groups, removing NA values
# group1 <- na.omit(data_final$Days.Since.Update[data_final$Content.Rating == content_ratings[i]])
# group2 <- na.omit(data_final$Days.Since.Update[data_final$Content.Rating == content_ratings[j]])
#
# # Check if both groups have enough data for comparison
# if(length(group1) > 1 && length(group2) > 1) {
# ks_test <- ks.test(group1, group2)
# ks_results <- rbind(ks_results,
# data.frame(rating1 = content_ratings[i],
# rating2 = content_ratings[j],
# p_value = ks_test$p.value))
# }
# }
# }
#
# print("\nKolmogorov-Smirnov Test Results:")
# print(ks_results[ks_results$p_value < 0.05,])Visualization for Content Rating vs Installs
# 1. Basic statistics for Installs by Content Rating
installs_by_rating <- data_final %>%
group_by(Content.Rating) %>%
summarise(
mean_installs = mean(Installs, na.rm = TRUE),
median_installs = median(Installs, na.rm = TRUE),
total_installs = sum(Installs, na.rm = TRUE),
n_apps = n()
) %>%
arrange(desc(mean_installs))
print("Summary of Installs by Content Rating:")## [1] "Summary of Installs by Content Rating:"print(installs_by_rating)## # A tibble: 6 × 5
## Content.Rating mean_installs median_installs total_installs n_apps
## <fct> <dbl> <dbl> <dbl> <int>
## 1 teen 15914358. 500000 16487275393 1036
## 2 everyone 10+ 12472894. 1000000 4016271795 322
## 3 everyone 6602474. 50000 52179352961 7903
## 4 mature 17+ 6203529. 500000 2437986878 393
## 5 adults only 18+ 666667. 500000 2000000 3
## 6 unrated 25250 25250 50500 2# 2. Visualize distribution of installs by content rating
ggplot(data_final, aes(x = Content.Rating, y = log10(Installs))) +
geom_boxplot(fill = "lightblue") +
labs(title = "Distribution of App Installs by Content Rating",
x = "Content Rating",
y = "Log10(Number of Installs)") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Visualization for Last Updated vs Installs
data_analysis <- data_final %>%
mutate(
days_since_update = as.numeric(difftime(max(Last.Updated), Last.Updated, units = "days")),
update_year = year(Last.Updated),
update_month = month(Last.Updated)
)
data_analysis <- data_analysis %>%
mutate(update_recency = ifelse(days_since_update <= median(days_since_update),
"Recent Update", "Old Update"))
recent_vs_old <- data_analysis %>%
group_by(Content.Rating, update_recency) %>%
summarise(
mean_installs = mean(Installs, na.rm = TRUE),
median_installs = median(Installs, na.rm = TRUE),
n_apps = n()
)
print("\nComparison of Installs by Update Recency and Content Rating:")## [1] "\nComparison of Installs by Update Recency and Content Rating:"print(recent_vs_old)## # A tibble: 10 × 5
## # Groups: Content.Rating [6]
## Content.Rating update_recency mean_installs median_installs n_apps
## <fct> <chr> <dbl> <dbl> <int>
## 1 adults only 18+ Recent Update 666667. 500000 3
## 2 everyone Old Update 1787608. 10000 4110
## 3 everyone Recent Update 11819742. 500000 3793
## 4 everyone 10+ Old Update 2711120. 100000 135
## 5 everyone 10+ Recent Update 19520163. 1000000 187
## 6 mature 17+ Old Update 875646. 100000 118
## 7 mature 17+ Recent Update 8489675. 500000 275
## 8 teen Old Update 1625562. 50000 441
## 9 teen Recent Update 26504878. 1000000 595
## 10 unrated Old Update 25250 25250 2# 7. Visualization of update recency effect
ggplot(data_analysis, aes(x = Content.Rating, y = log10(Installs), fill = update_recency)) +
geom_boxplot() +
labs(title = "Install Distribution by Content Rating and Update Recency",
x = "Content Rating",
y = "Log10(Number of Installs)",
fill = "Update Recency") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
Visualization for Last Updated vs Content Rating vs Installs
# 3. Timeline analysis: Average installs over time by content rating
installs_timeline <- data_final %>%
group_by(Content.Rating, Last.Updated) %>%
summarise(avg_installs = mean(Installs, na.rm = TRUE)) %>%
ungroup()
ggplot(installs_timeline, aes(x = Last.Updated, y = log10(avg_installs), color = Content.Rating)) +
geom_smooth(method = "loess", se = FALSE) +
labs(title = "Average App Installs Over Time by Content Rating",
x = "Last Updated Date",
y = "Log10(Average Installs)") +
theme_minimal() +
theme(legend.position = "bottom")
Statistical Tests
Statistical test for Installs and Price
# Check for missing values and ensure no negative/zero values in log_Installs
#data_final <- data_final %>%
#filter(!is.na(Installs), Installs > 0) # Remove missing values and zeros in Installs
# Apply log transformation, adding 1 to avoid log(0)
data_final$log_Installs <- log(data_final$Installs + 1)
# Ensure Price_Category has no missing values
data_final <- data_final %>%
filter(!is.na(Price_Category))
#Perform t-test on log-transformed Installs by Price Category
t_test_result <- t.test(log_Installs ~ Price_Category, data = data_final, var.equal = FALSE)
#Print t-test results
print(t_test_result)##
## Welch Two Sample t-test
##
## data: log_Installs by Price_Category
## t = 29.262, df = 981.81, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Free and group Paid is not equal to 0
## 95 percent confidence interval:
## 3.552682 4.063439
## sample estimates:
## mean in group Free mean in group Paid
## 10.996530 7.188469There is a statistically significant difference between the number of installs for “Free” and “Paid” apps, with the p-value being extremely small.
From the above analysis, we can practically state that free apps are more popular than paid apps, which can be considered true in the app market.
T-Test for Reviews and Price
#Confirming with a t-test
# Perform t-test for Reviews between Free and Paid
t_test_reviews <- t.test(Reviews ~ Price_Category, data = data_final)
# Perform t-test for Rating between Free and Paid
t_test_rating <- t.test(Rating ~ Price_Category, data = data_final)
# Print the results
print(t_test_reviews)##
## Welch Two Sample t-test
##
## data: Reviews by Price_Category
## t = 11.019, df = 9299.1, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Free and group Paid is not equal to 0
## 95 percent confidence interval:
## 185401.3 265636.3
## sample estimates:
## mean in group Free mean in group Paid
## 234243.689 8724.888print(t_test_rating)##
## Welch Two Sample t-test
##
## data: Rating by Price_Category
## t = -3.9443, df = 883.57, p-value = 8.638e-05
## alternative hypothesis: true difference in means between group Free and group Paid is not equal to 0
## 95 percent confidence interval:
## -0.1121028 -0.0376075
## sample estimates:
## mean in group Free mean in group Paid
## 4.167384 4.242239There is a statistically significant difference between the mean number of reviews for Free and Paid apps. Free apps have significantly more reviews on average.
There is a statistically significant difference between the mean ratings for Free and Paid apps. Paid apps have slightly higher ratings on average, though the difference is small.
ANOVA Test for Reviews vs Ratings
The tests below are to test whether or not different review categories have different average ratings.
anova_result <- aov(Rating ~ as.factor(Review_Category), data = data_clean)
summary(anova_result)## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(Review_Category) 11 106.3 9.662 41.36 <2e-16 ***
## Residuals 9647 2253.6 0.234
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to p-value, it is significant hence we can say that the average rating for all review categories is not same.
Post Hoc Test - Review Category
# Perform Tukey's HSD
tukey_result <- TukeyHSD(anova_result)
tukey_result## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Rating ~ as.factor(Review_Category), data = data_clean)
##
## $`as.factor(Review_Category)`
## diff lwr upr p adj
## 100+-0+ -0.096683215 -0.152307271 -0.04105916 0.0000009
## 500+-0+ -0.063032835 -0.141474646 0.01540898 0.2646281
## 1K+-0+ -0.019190832 -0.089971134 0.05158947 0.9992526
## 2.5K+-0+ 0.003350463 -0.074143085 0.08084401 1.0000000
## 5K+-0+ 0.064918154 -0.012646893 0.14248320 0.2087515
## 10K+-0+ 0.095614797 0.030638525 0.16059107 0.0000973
## 25K+-0+ 0.105627098 0.035846939 0.17540726 0.0000488
## 50K+-0+ 0.167554014 0.091642554 0.24346547 0.0000000
## 100K+-0+ 0.203608898 0.135724795 0.27149300 0.0000000
## 300K+-0+ 0.249388670 0.170111342 0.32866600 0.0000000
## 1M+-0+ 0.300139945 0.211244127 0.38903576 0.0000000
## 500+-100+ 0.033650380 -0.054364565 0.12166533 0.9848292
## 1K+-100+ 0.077492383 -0.003768703 0.15875347 0.0784345
## 2.5K+-100+ 0.100033678 0.012862795 0.18720456 0.0096675
## 5K+-100+ 0.161601369 0.074366918 0.24883582 0.0000001
## 10K+-100+ 0.192298012 0.116039053 0.26855697 0.0000000
## 25K+-100+ 0.202310313 0.121918874 0.28270175 0.0000000
## 50K+-100+ 0.264237229 0.178469737 0.35000472 0.0000000
## 100K+-100+ 0.300292113 0.221540831 0.37904339 0.0000000
## 300K+-100+ 0.346071885 0.257311491 0.43483228 0.0000000
## 1M+-100+ 0.396823160 0.299375844 0.49427048 0.0000000
## 1K+-500+ 0.043842003 -0.054455739 0.14213974 0.9515761
## 2.5K+-500+ 0.066383298 -0.036853541 0.16962014 0.6214468
## 5K+-500+ 0.127950989 0.024660470 0.23124151 0.0030189
## 10K+-500+ 0.158647632 0.064443010 0.25285225 0.0000025
## 25K+-500+ 0.168659933 0.071079887 0.26623998 0.0000011
## 50K+-500+ 0.230586849 0.128532233 0.33264146 0.0000000
## 100K+-500+ 0.266641733 0.170408442 0.36287502 0.0000000
## 300K+-500+ 0.312421505 0.207839051 0.41700396 0.0000000
## 1M+-500+ 0.363172780 0.251123410 0.47522215 0.0000000
## 2.5K+-1K+ 0.022541295 -0.075001405 0.12008400 0.9998394
## 5K+-1K+ 0.084108986 -0.013490527 0.18170850 0.1727899
## 10K+-1K+ 0.114805629 0.026878134 0.20273312 0.0012014
## 25K+-1K+ 0.124817930 0.033283243 0.21635262 0.0005180
## 50K+-1K+ 0.186744846 0.090454254 0.28303544 0.0000000
## 100K+-1K+ 0.222799730 0.132702117 0.31289734 0.0000000
## 300K+-1K+ 0.268579502 0.169613735 0.36754527 0.0000000
## 1M+-1K+ 0.319330777 0.212504774 0.42615678 0.0000000
## 5K+-2.5K+ 0.061567691 -0.041004546 0.16413993 0.7193424
## 10K+-2.5K+ 0.092264334 -0.001152170 0.18568084 0.0565429
## 25K+-2.5K+ 0.102276635 0.005457227 0.19909604 0.0276896
## 50K+-2.5K+ 0.164203551 0.062875978 0.26553112 0.0000078
## 100K+-2.5K+ 0.200258435 0.104796512 0.29572036 0.0000000
## 300K+-2.5K+ 0.246038206 0.142165102 0.34991131 0.0000000
## 1M+-2.5K+ 0.296789482 0.185401898 0.40817707 0.0000000
## 10K+-5K+ 0.030696643 -0.062779181 0.12417247 0.9957463
## 25K+-5K+ 0.040708944 -0.056167701 0.13758559 0.9685508
## 50K+-5K+ 0.102635860 0.001253596 0.20401812 0.0440982
## 100K+-5K+ 0.138690744 0.043170771 0.23421072 0.0001331
## 300K+-5K+ 0.184470516 0.080544059 0.28839697 0.0000004
## 1M+-5K+ 0.235221791 0.123784453 0.34665913 0.0000000
## 25K+-10K+ 0.010012302 -0.077112114 0.09713672 0.9999999
## 50K+-10K+ 0.071939217 -0.020169104 0.16404754 0.3070668
## 100K+-10K+ 0.107994101 0.022380758 0.19360745 0.0022235
## 300K+-10K+ 0.153773873 0.058872409 0.24867534 0.0000078
## 1M+-10K+ 0.204525148 0.101453039 0.30759726 0.0000000
## 50K+-25K+ 0.061926916 -0.033630908 0.15748474 0.6094814
## 100K+-25K+ 0.097981800 0.008667751 0.18729585 0.0175649
## 300K+-25K+ 0.143761571 0.045508620 0.24201452 0.0001113
## 1M+-25K+ 0.194512847 0.088346871 0.30067882 0.0000001
## 100K+-50K+ 0.036054884 -0.058127272 0.13023704 0.9846717
## 300K+-50K+ 0.081834656 -0.020863551 0.18453286 0.2768896
## 1M+-50K+ 0.132585931 0.022293168 0.24287869 0.0048805
## 300K+-100K+ 0.045779772 -0.051135776 0.14269532 0.9282456
## 1M+-100K+ 0.096531047 -0.008398431 0.20146052 0.1064662
## 1M+-300K+ 0.050751275 -0.061884591 0.16338714 0.9479902# Convert the result to a data frame
tukey_df <- as.data.frame(tukey_result$`as.factor(Review_Category)`)
# Filter for significant p-values
significant_tukey <- tukey_df[tukey_df[4] < 0.05, ]
# Display the significant results
print(significant_tukey)## diff lwr upr p adj
## 100+-0+ -0.09668322 -0.152307271 -0.04105916 8.987756e-07
## 10K+-0+ 0.09561480 0.030638525 0.16059107 9.732720e-05
## 25K+-0+ 0.10562710 0.035846939 0.17540726 4.884843e-05
## 50K+-0+ 0.16755401 0.091642554 0.24346547 0.000000e+00
## 100K+-0+ 0.20360890 0.135724795 0.27149300 0.000000e+00
## 300K+-0+ 0.24938867 0.170111342 0.32866600 0.000000e+00
## 1M+-0+ 0.30013994 0.211244127 0.38903576 0.000000e+00
## 2.5K+-100+ 0.10003368 0.012862795 0.18720456 9.667490e-03
## 5K+-100+ 0.16160137 0.074366918 0.24883582 9.538328e-08
## 10K+-100+ 0.19229801 0.116039053 0.26855697 0.000000e+00
## 25K+-100+ 0.20231031 0.121918874 0.28270175 0.000000e+00
## 50K+-100+ 0.26423723 0.178469737 0.35000472 0.000000e+00
## 100K+-100+ 0.30029211 0.221540831 0.37904339 0.000000e+00
## 300K+-100+ 0.34607188 0.257311491 0.43483228 0.000000e+00
## 1M+-100+ 0.39682316 0.299375844 0.49427048 0.000000e+00
## 5K+-500+ 0.12795099 0.024660470 0.23124151 3.018884e-03
## 10K+-500+ 0.15864763 0.064443010 0.25285225 2.473396e-06
## 25K+-500+ 0.16865993 0.071079887 0.26623998 1.080775e-06
## 50K+-500+ 0.23058685 0.128532233 0.33264146 0.000000e+00
## 100K+-500+ 0.26664173 0.170408442 0.36287502 0.000000e+00
## 300K+-500+ 0.31242150 0.207839051 0.41700396 0.000000e+00
## 1M+-500+ 0.36317278 0.251123410 0.47522215 0.000000e+00
## 10K+-1K+ 0.11480563 0.026878134 0.20273312 1.201416e-03
## 25K+-1K+ 0.12481793 0.033283243 0.21635262 5.179950e-04
## 50K+-1K+ 0.18674485 0.090454254 0.28303544 1.572425e-08
## 100K+-1K+ 0.22279973 0.132702117 0.31289734 0.000000e+00
## 300K+-1K+ 0.26857950 0.169613735 0.36754527 0.000000e+00
## 1M+-1K+ 0.31933078 0.212504774 0.42615678 0.000000e+00
## 25K+-2.5K+ 0.10227664 0.005457227 0.19909604 2.768961e-02
## 50K+-2.5K+ 0.16420355 0.062875978 0.26553112 7.808701e-06
## 100K+-2.5K+ 0.20025843 0.104796512 0.29572036 3.507881e-10
## 300K+-2.5K+ 0.24603821 0.142165102 0.34991131 0.000000e+00
## 1M+-2.5K+ 0.29678948 0.185401898 0.40817707 0.000000e+00
## 50K+-5K+ 0.10263586 0.001253596 0.20401812 4.409823e-02
## 100K+-5K+ 0.13869074 0.043170771 0.23421072 1.331239e-04
## 300K+-5K+ 0.18447052 0.080544059 0.28839697 4.428778e-07
## 1M+-5K+ 0.23522179 0.123784453 0.34665913 2.244944e-10
## 100K+-10K+ 0.10799410 0.022380758 0.19360745 2.223466e-03
## 300K+-10K+ 0.15377387 0.058872409 0.24867534 7.832139e-06
## 1M+-10K+ 0.20452515 0.101453039 0.30759726 5.942656e-09
## 100K+-25K+ 0.09798180 0.008667751 0.18729585 1.756493e-02
## 300K+-25K+ 0.14376157 0.045508620 0.24201452 1.113055e-04
## 1M+-25K+ 0.19451285 0.088346871 0.30067882 1.436204e-07
## 1M+-50K+ 0.13258593 0.022293168 0.24287869 4.880458e-03As we can see, the significant difference for average rating for different review categories is between 0+ and 1M+ as expected.
For easier Ratings and Reviews vs Installs we can group Installs into categories given
Test for Installs by Category
# Ensure that Category is treated as a factor
data_final$Category <- as.factor(data_final$Category)
# Perform one-way ANOVA
anova_result <- aov(log_Installs ~ Category, data = data_final)
# Summary of the ANOVA result
summary(anova_result)## Df Sum Sq Mean Sq F value Pr(>F)
## Category 32 21252 664.1 39.09 <2e-16 ***
## Residuals 9626 163522 17.0
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Since the ANOVA indicates significant differences among the groups, conducting a post-hoc analysis (Tukey’s HSD) to determine which specific categories differ from each other.
# Post-hoc test (as ANOVA is significant)
TukeyHSD(anova_result)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = log_Installs ~ Category, data = data_final)
##
## $Category
## diff lwr upr
## AUTO_AND_VEHICLES-ART_AND_DESIGN -1.333946079 -3.923524642 1.25563248
## BEAUTY-ART_AND_DESIGN -0.754689386 -3.660721545 2.15134277
## BOOKS_AND_REFERENCE-ART_AND_DESIGN -1.510577243 -3.730572003 0.70941752
## BUSINESS-ART_AND_DESIGN -3.461218500 -5.560851817 -1.36158518
## COMICS-ART_AND_DESIGN 0.199142684 -2.663993658 3.06227903
## COMMUNICATION-ART_AND_DESIGN 0.001519125 -2.143888145 2.14692640
## DATING-ART_AND_DESIGN -1.737471023 -4.030350864 0.55540882
## EDUCATION-ART_AND_DESIGN 2.174632189 -0.250846617 4.60011100
## ENTERTAINMENT-ART_AND_DESIGN 3.571787284 1.076621663 6.06695291
## EVENTS-ART_AND_DESIGN -3.101147241 -5.867199735 -0.33509475
## FAMILY-ART_AND_DESIGN -0.808748355 -2.798513651 1.18101694
## FINANCE-ART_AND_DESIGN -1.048969776 -3.178567267 1.08062771
## FOOD_AND_DRINK-ART_AND_DESIGN 0.241573356 -2.210270124 2.69341684
## GAME-ART_AND_DESIGN 1.898985933 -0.121119019 3.91909088
## HEALTH_AND_FITNESS-ART_AND_DESIGN -0.334869967 -2.497192668 1.82745273
## HOUSE_AND_HOME-ART_AND_DESIGN 0.554439863 -2.116530710 3.22541044
## LIBRARIES_AND_DEMO-ART_AND_DESIGN -1.020655132 -3.616846100 1.57553583
## LIFESTYLE-ART_AND_DESIGN -1.722814971 -3.841547747 0.39591781
## MAPS_AND_NAVIGATION-ART_AND_DESIGN -0.085300113 -2.471611303 2.30101108
## MEDICAL-ART_AND_DESIGN -3.682553432 -5.790954438 -1.57415242
## NEWS_AND_MAGAZINES-ART_AND_DESIGN -0.943248560 -3.131726240 1.24522912
## PARENTING-ART_AND_DESIGN -0.058770575 -2.870546041 2.75300489
## PERSONALIZATION-ART_AND_DESIGN -1.478643094 -3.594458795 0.63717261
## PHOTOGRAPHY-ART_AND_DESIGN 1.840400248 -0.326813802 4.00761430
## PRODUCTIVITY-ART_AND_DESIGN -0.567762994 -2.684401409 1.54887542
## SHOPPING-ART_AND_DESIGN 1.104670412 -1.139782785 3.34912361
## SOCIAL-ART_AND_DESIGN 0.055522421 -2.146733487 2.25777833
## SPORTS-ART_AND_DESIGN -0.684952080 -2.824778474 1.45487431
## TOOLS-ART_AND_DESIGN -0.499004900 -2.529170746 1.53116095
## TRAVEL_AND_LOCAL-ART_AND_DESIGN 0.002872826 -2.220521946 2.22626760
## VIDEO_PLAYERS-ART_AND_DESIGN 1.135736938 -1.172415812 3.44388969
## WEATHER-ART_AND_DESIGN 1.505772021 -1.125706885 4.13725093
## BEAUTY-AUTO_AND_VEHICLES 0.579256694 -2.159336677 3.31785006
## BOOKS_AND_REFERENCE-AUTO_AND_VEHICLES -0.176631164 -2.172438638 1.81917631
## BUSINESS-AUTO_AND_VEHICLES -2.127272421 -3.988275055 -0.26626979
## COMICS-AUTO_AND_VEHICLES 1.533088763 -1.159943069 4.22612060
## COMMUNICATION-AUTO_AND_VEHICLES 1.335465204 -0.577031357 3.24796176
## DATING-AUTO_AND_VEHICLES -0.403524944 -2.480101141 1.67305125
## EDUCATION-AUTO_AND_VEHICLES 3.508578268 1.286458069 5.73069847
## ENTERTAINMENT-AUTO_AND_VEHICLES 4.905733363 2.607751158 7.20371557
## EVENTS-AUTO_AND_VEHICLES -1.767201162 -4.356779725 0.82237740
## FAMILY-AUTO_AND_VEHICLES 0.525197724 -1.210900392 2.26129584
## FINANCE-AUTO_AND_VEHICLES 0.284976303 -1.609768062 2.17972067
## FOOD_AND_DRINK-AUTO_AND_VEHICLES 1.575519436 -0.675348662 3.82638753
## GAME-AUTO_AND_VEHICLES 3.232932012 1.462142709 5.00372132
## HEALTH_AND_FITNESS-AUTO_AND_VEHICLES 0.999076112 -0.932376762 2.93052899
## HOUSE_AND_HOME-AUTO_AND_VEHICLES 1.888385942 -0.599375007 4.37614689
## LIBRARIES_AND_DEMO-AUTO_AND_VEHICLES 0.313290947 -2.094005935 2.72058783
## LIFESTYLE-AUTO_AND_VEHICLES -0.388868892 -2.271393610 1.49365583
## MAPS_AND_NAVIGATION-AUTO_AND_VEHICLES 1.248645966 -0.930654801 3.42794673
## MEDICAL-AUTO_AND_VEHICLES -2.348607352 -4.219496324 -0.47771838
## NEWS_AND_MAGAZINES-AUTO_AND_VEHICLES 0.390697519 -1.569992486 2.35138752
## PARENTING-AUTO_AND_VEHICLES 1.275175505 -1.363186111 3.91353712
## PERSONALIZATION-AUTO_AND_VEHICLES -0.144697015 -2.023938037 1.73454401
## PHOTOGRAPHY-AUTO_AND_VEHICLES 3.174346327 1.237418999 5.11127366
## PRODUCTIVITY-AUTO_AND_VEHICLES 0.766183086 -1.113984174 2.64635034
## SHOPPING-AUTO_AND_VEHICLES 2.438616491 0.415638268 4.46159471
## SOCIAL-AUTO_AND_VEHICLES 1.389468500 -0.586588641 3.36552564
## SPORTS-AUTO_AND_VEHICLES 0.648993999 -1.257239915 2.55522791
## TOOLS-AUTO_AND_VEHICLES 0.834941179 -0.947316967 2.61719933
## TRAVEL_AND_LOCAL-AUTO_AND_VEHICLES 1.336818905 -0.662769816 3.33640763
## VIDEO_PLAYERS-AUTO_AND_VEHICLES 2.469683017 0.376255240 4.56311079
## WEATHER-AUTO_AND_VEHICLES 2.839718100 0.394405856 5.28503034
## BOOKS_AND_REFERENCE-BEAUTY -0.755887858 -3.148031926 1.63625621
## BUSINESS-BEAUTY -2.706529114 -4.987414157 -0.42564407
## COMICS-BEAUTY 0.953832069 -2.044755302 3.95241944
## COMMUNICATION-BEAUTY 0.756208511 -1.566881860 3.07929888
## DATING-BEAUTY -0.982781638 -3.442715473 1.47715220
## EDUCATION-BEAUTY 2.929321575 0.345347126 5.51329602
## ENTERTAINMENT-BEAUTY 4.326476670 1.676980870 6.97597247
## EVENTS-BEAUTY -2.346457856 -5.252490014 0.55957430
## FAMILY-BEAUTY -0.054058970 -2.234229248 2.12611131
## FINANCE-BEAUTY -0.294280390 -2.602778167 2.01421739
## FOOD_AND_DRINK-BEAUTY 0.996262742 -1.612475069 3.60500055
## GAME-BEAUTY 2.653675319 0.445780274 4.86157036
## HEALTH_AND_FITNESS-BEAUTY 0.419819418 -1.918901595 2.75854043
## HOUSE_AND_HOME-BEAUTY 1.309129248 -1.506551897 4.12481039
## LIBRARIES_AND_DEMO-BEAUTY -0.265965747 -3.010812564 2.47888107
## LIFESTYLE-BEAUTY -0.968125585 -3.266604449 1.33035328
## MAPS_AND_NAVIGATION-BEAUTY 0.669389273 -1.877855829 3.21663437
## MEDICAL-BEAUTY -2.927864046 -5.216822612 -0.63890548
## NEWS_AND_MAGAZINES-BEAUTY -0.188559175 -2.551483437 2.17436509
## PARENTING-BEAUTY 0.695918811 -2.253667226 3.64550485
## PERSONALIZATION-BEAUTY -0.723953708 -3.019743898 1.57183648
## PHOTOGRAPHY-BEAUTY 2.595089634 0.251845462 4.93833381
## PRODUCTIVITY-BEAUTY 0.186926392 -2.109622039 2.48347482
## SHOPPING-BEAUTY 1.859359797 -0.555499756 4.27421935
## SOCIAL-BEAUTY 0.810211806 -1.565479166 3.18590278
## SPORTS-BEAUTY 0.069737306 -2.248200034 2.38767464
## TOOLS-BEAUTY 0.255684486 -1.961419453 2.47278842
## TRAVEL_AND_LOCAL-BEAUTY 0.757562212 -1.637737525 3.15286195
## VIDEO_PLAYERS-BEAUTY 1.890426323 -0.583749424 4.36460207
## WEATHER-BEAUTY 2.260461407 -0.517785837 5.03870865
## BUSINESS-BOOKS_AND_REFERENCE -1.950641256 -3.249021171 -0.65226134
## COMICS-BOOKS_AND_REFERENCE 1.709719927 -0.630126231 4.04956609
## COMMUNICATION-BOOKS_AND_REFERENCE 1.512096368 0.140928001 2.88326474
## DATING-BOOKS_AND_REFERENCE -0.226893780 -1.818945380 1.36515782
## EDUCATION-BOOKS_AND_REFERENCE 3.685209433 1.907492420 5.46292644
## ENTERTAINMENT-BOOKS_AND_REFERENCE 5.082364528 3.210685652 6.95404340
## EVENTS-BOOKS_AND_REFERENCE -1.590569998 -3.810564757 0.62942476
## FAMILY-BOOKS_AND_REFERENCE 0.701828888 -0.410149649 1.81380742
## FINANCE-BOOKS_AND_REFERENCE 0.461607468 -0.884689605 1.80790454
## FOOD_AND_DRINK-BOOKS_AND_REFERENCE 1.752150600 -0.061372709 3.56567391
## GAME-BOOKS_AND_REFERENCE 3.409563176 2.244164381 4.57496197
## HEALTH_AND_FITNESS-BOOKS_AND_REFERENCE 1.175707276 -0.221779683 2.57319424
## HOUSE_AND_HOME-BOOKS_AND_REFERENCE 2.065017106 -0.035319566 4.16535378
## LIBRARIES_AND_DEMO-BOOKS_AND_REFERENCE 0.489922111 -1.514457562 2.49430178
## LIFESTYLE-BOOKS_AND_REFERENCE -0.212237727 -1.541282088 1.11680663
## MAPS_AND_NAVIGATION-BOOKS_AND_REFERENCE 1.425277131 -0.298617133 3.14917139
## MEDICAL-BOOKS_AND_REFERENCE -2.171976188 -3.484487194 -0.85946518
## NEWS_AND_MAGAZINES-BOOKS_AND_REFERENCE 0.567328683 -0.870296056 2.00495342
## PARENTING-BOOKS_AND_REFERENCE 1.451806669 -0.824904031 3.72851737
## PERSONALIZATION-BOOKS_AND_REFERENCE 0.031934150 -1.292454924 1.35632322
## PHOTOGRAPHY-BOOKS_AND_REFERENCE 3.350977492 1.945934050 4.75602093
## PRODUCTIVITY-BOOKS_AND_REFERENCE 0.942814250 -0.382888779 2.26851728
## SHOPPING-BOOKS_AND_REFERENCE 2.615247655 1.093767952 4.13672736
## SOCIAL-BOOKS_AND_REFERENCE 1.566099664 0.107586236 3.02461309
## SPORTS-BOOKS_AND_REFERENCE 0.825625163 -0.536794498 2.18804482
## TOOLS-BOOKS_AND_REFERENCE 1.011572343 -0.171180250 2.19432494
## TRAVEL_AND_LOCAL-BOOKS_AND_REFERENCE 1.513450070 0.023210273 3.00368987
## VIDEO_PLAYERS-BOOKS_AND_REFERENCE 2.646314181 1.032344091 4.26028427
## WEATHER-BOOKS_AND_REFERENCE 3.016349264 0.966468398 5.06623013
## COMICS-BUSINESS 3.660361184 1.434386480 5.88633589
## COMMUNICATION-BUSINESS 3.462737625 2.296467491 4.62900776
## DATING-BUSINESS 1.723747477 0.304342097 3.14315286
## EDUCATION-BUSINESS 5.635850689 4.010931888 7.26076949
## ENTERTAINMENT-BUSINESS 7.033005784 5.305792668 8.76021890
## EVENTS-BUSINESS 0.360071259 -1.739562058 2.45970458
## FAMILY-BUSINESS 2.652470144 1.805959896 3.49898039
## FINANCE-BUSINESS 2.412248724 1.275323422 3.54917403
## FOOD_AND_DRINK-BUSINESS 3.702791856 2.038775593 5.36680812
## GAME-BUSINESS 5.360204433 4.444651219 6.27575765
## HEALTH_AND_FITNESS-BUSINESS 3.126348533 1.929246559 4.32345051
## HOUSE_AND_HOME-BUSINESS 4.015658362 2.042970483 5.98834624
## LIBRARIES_AND_DEMO-BUSINESS 2.440563367 0.570370541 4.31075619
## LIFESTYLE-BUSINESS 1.738403529 0.621961749 2.85484531
## MAPS_AND_NAVIGATION-BUSINESS 3.375918387 1.810065659 4.94177112
## MEDICAL-BUSINESS -0.221334932 -1.318042949 0.87537309
## NEWS_AND_MAGAZINES-BUSINESS 2.517969939 1.274246407 3.76169347
## PARENTING-BUSINESS 3.402447925 1.242935261 5.56196059
## PERSONALIZATION-BUSINESS 1.982575406 0.871679482 3.09347133
## PHOTOGRAPHY-BUSINESS 5.301618748 4.095703988 6.50753351
## PRODUCTIVITY-BUSINESS 2.893455506 1.780993438 4.00591757
## SHOPPING-BUSINESS 4.565888912 3.226118848 5.90565897
## SOCIAL-BUSINESS 3.516740920 2.248929912 4.78455193
## SPORTS-BUSINESS 2.776266420 1.620294678 3.93223816
## TOOLS-BUSINESS 2.962213600 2.024670517 3.89975668
## TRAVEL_AND_LOCAL-BUSINESS 3.464091326 2.159906529 4.76827612
## VIDEO_PLAYERS-BUSINESS 4.596955437 3.153008490 6.04090238
## WEATHER-BUSINESS 4.966990521 3.048111967 6.88586907
## COMMUNICATION-COMICS -0.197623559 -2.466825108 2.07157799
## DATING-COMICS -1.936613707 -4.345721690 0.47249428
## EDUCATION-COMICS 1.975489505 -0.560146658 4.51112567
## ENTERTAINMENT-COMICS 3.372644600 0.770269763 5.97501944
## EVENTS-COMICS -3.300289925 -6.163426266 -0.43715358
## FAMILY-COMICS -1.007891039 -3.130547216 1.11476514
## FINANCE-COMICS -1.248112460 -3.502372601 1.00614768
## FOOD_AND_DRINK-COMICS 0.042430673 -2.518436323 2.60329767
## GAME-COMICS 1.699843249 -0.451279093 3.85096559
## HEALTH_AND_FITNESS-COMICS -0.534012651 -2.819213469 1.75118817
## HOUSE_AND_HOME-COMICS 0.355297179 -2.416090040 3.12668440
## LIBRARIES_AND_DEMO-COMICS -1.219797816 -3.919188646 1.47959301
## LIFESTYLE-COMICS -1.921957655 -4.165956739 0.32204143
## MAPS_AND_NAVIGATION-COMICS -0.284442797 -2.782639028 2.21375343
## MEDICAL-COMICS -3.881696115 -6.115942771 -1.64744946
## NEWS_AND_MAGAZINES-COMICS -1.142391244 -3.452356150 1.16757366
## PARENTING-COMICS -0.257913258 -3.165246158 2.64941964
## PERSONALIZATION-COMICS -1.677785778 -3.919030833 0.56345928
## PHOTOGRAPHY-COMICS 1.641257564 -0.648572135 3.93108726
## PRODUCTIVITY-COMICS -0.766905677 -3.008927421 1.47511607
## SHOPPING-COMICS 0.905527728 -1.457536695 3.26859215
## SOCIAL-COMICS -0.143620263 -2.466642949 2.17940242
## SPORTS-COMICS -0.884094764 -3.148020626 1.37983110
## TOOLS-COMICS -0.698147584 -2.858720812 1.46242564
## TRAVEL_AND_LOCAL-COMICS -0.196269858 -2.539342120 2.14680241
## VIDEO_PLAYERS-COMICS 0.936594254 -1.487054324 3.36024283
## WEATHER-COMICS 1.306629337 -1.426717429 4.03997610
## DATING-COMMUNICATION -1.738990148 -3.225268696 -0.25271160
## EDUCATION-COMMUNICATION 2.173113064 0.489464230 3.85676190
## ENTERTAINMENT-COMMUNICATION 3.570268159 1.787692091 5.35284423
## EVENTS-COMMUNICATION -3.102666366 -5.248073636 -0.95725910
## FAMILY-COMMUNICATION -0.810267480 -1.764674044 0.14413908
## FINANCE-COMMUNICATION -1.050488901 -2.269878679 0.16890088
## FOOD_AND_DRINK-COMMUNICATION 0.240054231 -1.481358681 1.96146714
## GAME-COMMUNICATION 1.897466808 0.881322145 2.91361147
## HEALTH_AND_FITNESS-COMMUNICATION -0.336389092 -1.612071429 0.93929324
## HOUSE_AND_HOME-COMMUNICATION 0.552920738 -1.468417868 2.57425934
## LIBRARIES_AND_DEMO-COMMUNICATION -1.022174257 -2.943614732 0.89926622
## LIFESTYLE-COMMUNICATION -1.724334096 -2.924648445 -0.52401975
## MAPS_AND_NAVIGATION-COMMUNICATION -0.086819238 -1.713535887 1.53989741
## MEDICAL-COMMUNICATION -3.684072556 -4.866054267 -2.50209085
## NEWS_AND_MAGAZINES-COMMUNICATION -0.944767685 -2.264298100 0.37476273
## PARENTING-COMMUNICATION -0.060289699 -2.264333083 2.14375368
## PERSONALIZATION-COMMUNICATION -1.480162219 -2.675319967 -0.28500447
## PHOTOGRAPHY-COMMUNICATION 1.838881123 0.554925245 3.12283700
## PRODUCTIVITY-COMMUNICATION -0.569282118 -1.765895733 0.62733150
## SHOPPING-COMMUNICATION 1.103151287 -0.307272802 2.51357538
## SOCIAL-COMMUNICATION 0.054003296 -1.288254892 1.39626148
## SPORTS-COMMUNICATION -0.686471205 -1.923638516 0.55069611
## TOOLS-COMMUNICATION -0.500524025 -1.536525627 0.53547758
## TRAVEL_AND_LOCAL-COMMUNICATION 0.001353701 -1.375312662 1.37802006
## VIDEO_PLAYERS-COMMUNICATION 1.134217813 -0.375515633 2.64395126
## WEATHER-COMMUNICATION 1.504252896 -0.464606467 3.47311226
## EDUCATION-DATING 3.912103212 2.044163437 5.78004299
## ENTERTAINMENT-DATING 5.309258307 3.351682499 7.26683412
## EVENTS-DATING -1.363676218 -3.656556058 0.92920362
## FAMILY-DATING 0.928722668 -0.322443786 2.17988912
## FINANCE-DATING 0.688501247 -0.774863724 2.15186622
## FOOD_AND_DRINK-DATING 1.979044380 0.076996005 3.88109275
## GAME-DATING 3.636456956 2.337582219 4.93533169
## HEALTH_AND_FITNESS-DATING 1.402601056 -0.107991884 2.91319400
## HOUSE_AND_HOME-DATING 2.291910886 0.114679762 4.46914201
## LIBRARIES_AND_DEMO-DATING 0.716815891 -1.368000433 2.80163222
## LIFESTYLE-DATING 0.014656052 -1.432852201 1.46216431
## MAPS_AND_NAVIGATION-DATING 1.652170910 -0.164620950 3.46896277
## MEDICAL-DATING -1.945082408 -3.377425374 -0.51273944
## NEWS_AND_MAGAZINES-DATING 0.794222463 -0.753577951 2.34202288
## PARENTING-DATING 1.678700449 -0.669135329 4.02653623
## PERSONALIZATION-DATING 0.258827929 -1.184407204 1.70206306
## PHOTOGRAPHY-DATING 3.577871271 2.060284930 5.09545761
## PRODUCTIVITY-DATING 1.169708030 -0.274732952 2.61414901
## SHOPPING-DATING 2.842141435 1.216158127 4.46812474
## SOCIAL-DATING 1.792993444 0.225772129 3.36021476
## SPORTS-DATING 1.052518943 -0.425692328 2.53073021
## TOOLS-DATING 1.238466123 -0.076001422 2.55293367
## TRAVEL_AND_LOCAL-DATING 1.740343849 0.143554608 3.33713309
## VIDEO_PLAYERS-DATING 2.873207961 1.160368014 4.58604791
## WEATHER-DATING 3.243243044 1.114644257 5.37184183
## ENTERTAINMENT-EDUCATION 1.397155095 -0.714183940 3.50849413
## EVENTS-EDUCATION -5.275779430 -7.701258236 -2.85030062
## FAMILY-EDUCATION -2.983380544 -4.463605856 -1.50315523
## FINANCE-EDUCATION -3.223601965 -4.887058161 -1.56014577
## FOOD_AND_DRINK-EDUCATION -1.933058833 -3.993019390 0.12690172
## GAME-EDUCATION -0.275646256 -1.796410886 1.24511837
## HEALTH_AND_FITNESS-EDUCATION -2.509502156 -4.214653325 -0.80435099
## HOUSE_AND_HOME-EDUCATION -1.620192326 -3.936651876 0.69626722
## LIBRARIES_AND_DEMO-EDUCATION -3.195287321 -5.425109866 -0.96546478
## LIFESTYLE-EDUCATION -3.897447160 -5.546971218 -2.24792310
## MAPS_AND_NAVIGATION-EDUCATION -2.259932302 -4.241442367 -0.27842224
## MEDICAL-EDUCATION -5.857185621 -7.493417831 -4.22095341
## NEWS_AND_MAGAZINES-EDUCATION -3.117880749 -4.856079702 -1.37968180
## PARENTING-EDUCATION -2.233402764 -4.710897934 0.24409241
## PERSONALIZATION-EDUCATION -3.653275283 -5.299050822 -2.00749974
## PHOTOGRAPHY-EDUCATION -0.334231941 -2.045581636 1.37711775
## PRODUCTIVITY-EDUCATION -2.742395183 -4.389228273 -1.09556209
## SHOPPING-EDUCATION -1.069961777 -2.878129688 0.73820613
## SOCIAL-EDUCATION -2.119109768 -3.874624544 -0.36359499
## SPORTS-EDUCATION -2.859584269 -4.536115820 -1.18305272
## TOOLS-EDUCATION -2.673637089 -4.207740868 -1.13953331
## TRAVEL_AND_LOCAL-EDUCATION -2.171759363 -3.953720462 -0.38979826
## VIDEO_PLAYERS-EDUCATION -1.038895252 -2.925551065 0.84776056
## WEATHER-EDUCATION -0.668860168 -2.939671097 1.60195076
## EVENTS-ENTERTAINMENT -6.672934525 -9.168100147 -4.17776890
## FAMILY-ENTERTAINMENT -4.380535640 -5.972380799 -2.78869048
## FINANCE-ENTERTAINMENT -4.620757060 -6.384273591 -2.85724053
## FOOD_AND_DRINK-ENTERTAINMENT -3.330213928 -5.471788474 -1.18863938
## GAME-ENTERTAINMENT -1.672801351 -3.302411458 -0.04319124
## HEALTH_AND_FITNESS-ENTERTAINMENT -3.906657251 -5.709556180 -2.10375832
## HOUSE_AND_HOME-ENTERTAINMENT -3.017347422 -5.406675546 -0.62801930
## LIBRARIES_AND_DEMO-ENTERTAINMENT -4.592442417 -6.897873531 -2.28701130
## LIFESTYLE-ENTERTAINMENT -5.294602255 -7.044983259 -3.54422125
## MAPS_AND_NAVIGATION-ENTERTAINMENT -3.657087397 -5.723312501 -1.59086229
## MEDICAL-ENTERTAINMENT -7.254340716 -8.992201437 -5.51647999
## NEWS_AND_MAGAZINES-ENTERTAINMENT -4.515035845 -6.349222214 -2.68084948
## PARENTING-ENTERTAINMENT -3.630557859 -6.176316362 -1.08479936
## PERSONALIZATION-ENTERTAINMENT -5.050430378 -6.797279303 -3.30358145
## PHOTOGRAPHY-ENTERTAINMENT -1.731387036 -3.540149547 0.07737547
## PRODUCTIVITY-ENTERTAINMENT -4.139550278 -5.887395599 -2.39170496
## SHOPPING-ENTERTAINMENT -2.467116872 -4.367741831 -0.56649191
## SOCIAL-ENTERTAINMENT -3.516264864 -5.366869134 -1.66566059
## SPORTS-ENTERTAINMENT -4.256739364 -6.032594674 -2.48088405
## TOOLS-ENTERTAINMENT -4.070792184 -5.712857483 -2.42872689
## TRAVEL_AND_LOCAL-ENTERTAINMENT -3.568914458 -5.444624830 -1.69320409
## VIDEO_PLAYERS-ENTERTAINMENT -2.436050347 -4.411493132 -0.46060756
## WEATHER-ENTERTAINMENT -2.066015263 -4.411113623 0.27908310
## FAMILY-EVENTS 2.292398886 0.302633591 4.28216418
## FINANCE-EVENTS 2.052177465 -0.077420025 4.18177496
## FOOD_AND_DRINK-EVENTS 3.342720597 0.890877117 5.79456408
## GAME-EVENTS 5.000133174 2.980028222 7.02023813
## HEALTH_AND_FITNESS-EVENTS 2.766277274 0.603954573 4.92859998
## HOUSE_AND_HOME-EVENTS 3.655587104 0.984616531 6.32655768
## LIBRARIES_AND_DEMO-EVENTS 2.080492109 -0.515698858 4.67668308
## LIFESTYLE-EVENTS 1.378332270 -0.740400506 3.49706505
## MAPS_AND_NAVIGATION-EVENTS 3.015847128 0.629535938 5.40215832
## MEDICAL-EVENTS -0.581406190 -2.689807197 1.52699482
## NEWS_AND_MAGAZINES-EVENTS 2.157898681 -0.030578999 4.34637636
## PARENTING-EVENTS 3.042376667 0.230601200 5.85415213
## PERSONALIZATION-EVENTS 1.622504147 -0.493311554 3.73831985
## PHOTOGRAPHY-EVENTS 4.941547489 2.774333440 7.10876154
## PRODUCTIVITY-EVENTS 2.533384248 0.416745832 4.65002266
## SHOPPING-EVENTS 4.205817653 1.961364456 6.45027085
## SOCIAL-EVENTS 3.156669662 0.954413754 5.35892557
## SPORTS-EVENTS 2.416195161 0.276368767 4.55602156
## TOOLS-EVENTS 2.602142341 0.571976496 4.63230819
## TRAVEL_AND_LOCAL-EVENTS 3.104020067 0.880625295 5.32741484
## VIDEO_PLAYERS-EVENTS 4.236884179 1.928731429 6.54503693
## WEATHER-EVENTS 4.606919262 1.975440356 7.23839817
## FINANCE-FAMILY -0.240221421 -1.158537818 0.67809498
## FOOD_AND_DRINK-FAMILY 1.050321712 -0.472719978 2.57336340
## GAME-FAMILY 2.707734288 2.084080899 3.33138768
## HEALTH_AND_FITNESS-FAMILY 0.473878388 -0.517967869 1.46572465
## HOUSE_AND_HOME-FAMILY 1.363188218 -0.492129365 3.21850580
## LIBRARIES_AND_DEMO-FAMILY -0.211906777 -1.957852673 1.53403912
## LIFESTYLE-FAMILY -0.914066616 -1.806898128 -0.02123510
## MAPS_AND_NAVIGATION-FAMILY 0.723448243 -0.691684483 2.13858097
## MEDICAL-FAMILY -2.873805076 -3.741834072 -2.00577608
## NEWS_AND_MAGAZINES-FAMILY -0.134500205 -1.182142362 0.91314195
## PARENTING-FAMILY 0.749977781 -1.302874091 2.80282965
## PERSONALIZATION-FAMILY -0.669894739 -1.555781648 0.21599217
## PHOTOGRAPHY-FAMILY 2.649148604 1.646683506 3.65161370
## PRODUCTIVITY-FAMILY 0.240985362 -0.646864692 1.12883542
## SHOPPING-FAMILY 1.913418767 0.753380110 3.07345742
## SOCIAL-FAMILY 0.864270776 -0.211856827 1.94039838
## SPORTS-FAMILY 0.123796275 -0.817998039 1.06559059
## TOOLS-FAMILY 0.309743455 -0.345766190 0.96525310
## TRAVEL_AND_LOCAL-FAMILY 0.811621182 -0.307129840 1.93037220
## VIDEO_PLAYERS-FAMILY 1.944485293 0.665544853 3.22342573
## WEATHER-FAMILY 2.314520376 0.516521276 4.11251948
## FOOD_AND_DRINK-FINANCE 1.290543132 -0.411125323 2.99221159
## GAME-FINANCE 2.947955709 1.965630359 3.93028106
## HEALTH_AND_FITNESS-FINANCE 0.714099809 -0.534811133 1.96301075
## HOUSE_AND_HOME-FINANCE 1.603409639 -0.401140904 3.60796018
## LIBRARIES_AND_DEMO-FINANCE 0.028314644 -1.875457038 1.93208633
## LIFESTYLE-FINANCE -0.673845195 -1.845667559 0.49797717
## MAPS_AND_NAVIGATION-FINANCE 0.963669663 -0.642138598 2.56947792
## MEDICAL-FINANCE -2.633583656 -3.786620464 -1.48054685
## NEWS_AND_MAGAZINES-FINANCE 0.105721216 -1.187945523 1.39938795
## PARENTING-FINANCE 0.990199201 -1.198458001 3.17885640
## PERSONALIZATION-FINANCE -0.429673318 -1.596213141 0.73686651
## PHOTOGRAPHY-FINANCE 2.889370024 1.632009370 4.14673068
## PRODUCTIVITY-FINANCE 0.481206782 -0.686824578 1.64923814
## SHOPPING-FINANCE 2.153640188 0.767382914 3.53989746
## SOCIAL-FINANCE 1.104492197 -0.212348781 2.42133317
## SPORTS-FINANCE 0.364017696 -0.845526050 1.57356144
## TOOLS-FINANCE 0.549964876 -0.452887275 1.55281703
## TRAVEL_AND_LOCAL-FINANCE 1.051842602 -0.300053619 2.40373882
## VIDEO_PLAYERS-FINANCE 2.184706713 0.697525422 3.67188800
## WEATHER-FINANCE 2.554741797 0.603121878 4.50636172
## GAME-FOOD_AND_DRINK 1.657412577 0.094942073 3.21988308
## HEALTH_AND_FITNESS-FOOD_AND_DRINK -0.576443324 -2.318892612 1.16600596
## HOUSE_AND_HOME-FOOD_AND_DRINK 0.312866506 -2.031184231 2.65691724
## LIBRARIES_AND_DEMO-FOOD_AND_DRINK -1.262228489 -3.520700892 0.99624391
## LIFESTYLE-FOOD_AND_DRINK -1.964388327 -3.652440055 -0.27633660
## MAPS_AND_NAVIGATION-FOOD_AND_DRINK -0.326873469 -2.340569363 1.68682242
## MEDICAL-FOOD_AND_DRINK -3.924126788 -5.599192417 -2.24906116
## NEWS_AND_MAGAZINES-FOOD_AND_DRINK -1.184821917 -2.959624613 0.58998078
## PARENTING-FOOD_AND_DRINK -0.300343931 -2.803656003 2.20296814
## PERSONALIZATION-FOOD_AND_DRINK -1.720216450 -3.404605402 -0.03582750
## PHOTOGRAPHY-FOOD_AND_DRINK 1.598826892 -0.149688706 3.34734249
## PRODUCTIVITY-FOOD_AND_DRINK -0.809336350 -2.494758624 0.87608592
## SHOPPING-FOOD_AND_DRINK 0.863097055 -0.980285761 2.70647987
## SOCIAL-FOOD_AND_DRINK -0.186050936 -1.977815748 1.60571388
## SPORTS-FOOD_AND_DRINK -0.926525436 -2.640977843 0.78792697
## TOOLS-FOOD_AND_DRINK -0.740578256 -2.316034831 0.83487832
## TRAVEL_AND_LOCAL-FOOD_AND_DRINK -0.238700530 -2.056384324 1.57898326
## VIDEO_PLAYERS-FOOD_AND_DRINK 0.894163581 -1.026268447 2.81459561
## WEATHER-FOOD_AND_DRINK 1.264198665 -1.034751376 3.56314871
## HEALTH_AND_FITNESS-GAME -2.233855900 -3.285244070 -1.18246773
## HOUSE_AND_HOME-GAME -1.344546070 -3.232365294 0.54327315
## LIBRARIES_AND_DEMO-GAME -2.919641065 -4.700086279 -1.13919585
## LIFESTYLE-GAME -3.621800904 -4.580344694 -2.66325711
## MAPS_AND_NAVIGATION-GAME -1.984286046 -3.441769739 -0.52680235
## MEDICAL-GAME -5.581539364 -6.517024493 -4.64605424
## NEWS_AND_MAGAZINES-GAME -2.842234493 -3.946413906 -1.73805508
## PARENTING-GAME -1.957756507 -4.040029039 0.12451602
## PERSONALIZATION-GAME -3.377629027 -4.329707649 -2.42555040
## PHOTOGRAPHY-GAME -0.058585685 -1.119997178 1.00282581
## PRODUCTIVITY-GAME -2.466748926 -3.420654479 -1.51284337
## SHOPPING-GAME -0.794315521 -2.005656832 0.41702579
## SOCIAL-GAME -1.843463512 -2.974705619 -0.71222141
## SPORTS-GAME -2.583938013 -3.588246042 -1.57962998
## TOOLS-GAME -2.397990833 -3.140520954 -1.65546071
## TRAVEL_AND_LOCAL-GAME -1.896113107 -3.067975699 -0.72425051
## VIDEO_PLAYERS-GAME -0.763248995 -2.088898548 0.56240056
## WEATHER-GAME -0.393213912 -2.224732094 1.43830427
## HOUSE_AND_HOME-HEALTH_AND_FITNESS 0.889309830 -1.149973591 2.92859325
## LIBRARIES_AND_DEMO-HEALTH_AND_FITNESS -0.685785165 -2.626094575 1.25452425
## LIFESTYLE-HEALTH_AND_FITNESS -1.387945004 -2.618238320 -0.15765169
## MAPS_AND_NAVIGATION-HEALTH_AND_FITNESS 0.249569854 -1.399391687 1.89853140
## MEDICAL-HEALTH_AND_FITNESS -3.347683464 -4.560097532 -2.13526940
## NEWS_AND_MAGAZINES-HEALTH_AND_FITNESS -0.608378593 -1.955237020 0.73847983
## PARENTING-HEALTH_AND_FITNESS 0.276099393 -1.944412788 2.49661157
## PERSONALIZATION-HEALTH_AND_FITNESS -1.143773127 -2.369036017 0.08148976
## PHOTOGRAPHY-HEALTH_AND_FITNESS 2.175270215 0.863245137 3.48729529
## PRODUCTIVITY-HEALTH_AND_FITNESS -0.232893026 -1.459576055 0.99379000
## SHOPPING-HEALTH_AND_FITNESS 1.439540379 0.003516974 2.87556378
## SOCIAL-HEALTH_AND_FITNESS 0.390392388 -0.978740240 1.75952502
## SPORTS-HEALTH_AND_FITNESS -0.350082113 -1.616356201 0.91619197
## TOOLS-HEALTH_AND_FITNESS -0.164134933 -1.234726558 0.90645669
## TRAVEL_AND_LOCAL-HEALTH_AND_FITNESS 0.337742793 -1.065139020 1.74062461
## VIDEO_PLAYERS-HEALTH_AND_FITNESS 1.470606905 -0.063069131 3.00428294
## WEATHER-HEALTH_AND_FITNESS 1.840641988 -0.146636125 3.82792010
## LIBRARIES_AND_DEMO-HOUSE_AND_HOME -1.575094995 -4.069738245 0.91954825
## LIFESTYLE-HOUSE_AND_HOME -2.277254834 -4.270259094 -0.28425057
## MAPS_AND_NAVIGATION-HOUSE_AND_HOME -0.639739976 -2.915156092 1.63567614
## MEDICAL-HOUSE_AND_HOME -4.236993294 -6.219010501 -2.25497609
## NEWS_AND_MAGAZINES-HOUSE_AND_HOME -1.497688423 -3.564684301 0.56930746
## PARENTING-HOUSE_AND_HOME -0.613210437 -3.331503777 2.10508290
## PERSONALIZATION-HOUSE_AND_HOME -2.033082957 -4.022985841 -0.04318007
## PHOTOGRAPHY-HOUSE_AND_HOME 1.285960385 -0.758508774 3.33042954
## PRODUCTIVITY-HOUSE_AND_HOME -1.122202856 -3.112980490 0.86857478
## SHOPPING-HOUSE_AND_HOME 0.550230549 -1.575941494 2.67640259
## SOCIAL-HOUSE_AND_HOME -0.498917442 -2.580495807 1.58266092
## SPORTS-HOUSE_AND_HOME -1.239391943 -3.254806144 0.77602226
## TOOLS-HOUSE_AND_HOME -1.053444763 -2.952026014 0.84513649
## TRAVEL_AND_LOCAL-HOUSE_AND_HOME -0.551567036 -2.655497102 1.55236303
## VIDEO_PLAYERS-HOUSE_AND_HOME 0.581297075 -1.612012416 2.77460657
## WEATHER-HOUSE_AND_HOME 0.951332158 -1.580015040 3.48267936
## LIFESTYLE-LIBRARIES_AND_DEMO -0.702159839 -2.593770190 1.18945051
## MAPS_AND_NAVIGATION-LIBRARIES_AND_DEMO 0.935355019 -1.251798894 3.12250893
## MEDICAL-LIBRARIES_AND_DEMO -2.661898299 -4.541929136 -0.78186746
## NEWS_AND_MAGAZINES-LIBRARIES_AND_DEMO 0.077406572 -1.892008493 2.04682164
## PARENTING-LIBRARIES_AND_DEMO 0.961884558 -1.682967502 3.60673662
## PERSONALIZATION-LIBRARIES_AND_DEMO -0.457987962 -2.346330416 1.43035449
## PHOTOGRAPHY-LIBRARIES_AND_DEMO 2.861055380 0.915296433 4.80681433
## PRODUCTIVITY-LIBRARIES_AND_DEMO 0.452892139 -1.436372090 2.34215637
## SHOPPING-LIBRARIES_AND_DEMO 2.125325544 0.093889772 4.15676132
## SOCIAL-LIBRARIES_AND_DEMO 1.076177553 -0.908537093 3.06089220
## SPORTS-LIBRARIES_AND_DEMO 0.335703052 -1.579504023 2.25091013
## TOOLS-LIBRARIES_AND_DEMO 0.521650232 -1.270202023 2.31350249
## TRAVEL_AND_LOCAL-LIBRARIES_AND_DEMO 1.023527959 -0.984616822 3.03167274
## VIDEO_PLAYERS-LIBRARIES_AND_DEMO 2.156392070 0.054790238 4.25799390
## WEATHER-LIBRARIES_AND_DEMO 2.526427153 0.074113475 4.97874083
## MAPS_AND_NAVIGATION-LIFESTYLE 1.637514858 0.046143350 3.22888637
## MEDICAL-LIFESTYLE -1.959738461 -3.092583104 -0.82689382
## NEWS_AND_MAGAZINES-LIFESTYLE 0.779566411 -0.496136037 2.05526886
## PARENTING-LIFESTYLE 1.664044396 -0.514042713 3.84213151
## PERSONALIZATION-LIFESTYLE 0.244171877 -0.902413603 1.39075736
## PHOTOGRAPHY-LIFESTYLE 3.563215219 2.324345202 4.80208524
## PRODUCTIVITY-LIFESTYLE 1.155051977 0.006949036 2.30315492
## SHOPPING-LIFESTYLE 2.827485383 1.457977321 4.19699344
## SOCIAL-LIFESTYLE 1.778337392 0.479140230 3.07753455
## SPORTS-LIFESTYLE 1.037862891 -0.152447647 2.22817343
## TOOLS-LIFESTYLE 1.223810071 0.244241012 2.20337913
## TRAVEL_AND_LOCAL-LIFESTYLE 1.725687797 0.390971911 3.06040368
## VIDEO_PLAYERS-LIFESTYLE 2.858551909 1.386970685 4.33013313
## WEATHER-LIFESTYLE 3.228586992 1.288828395 5.16834559
## MEDICAL-MAPS_AND_NAVIGATION -3.597253319 -5.174843096 -2.01966354
## NEWS_AND_MAGAZINES-MAPS_AND_NAVIGATION -0.857948447 -2.541061413 0.82516452
## PARENTING-MAPS_AND_NAVIGATION 0.026529538 -2.412633428 2.46569250
## PERSONALIZATION-MAPS_AND_NAVIGATION -1.393342981 -2.980828661 0.19414270
## PHOTOGRAPHY-MAPS_AND_NAVIGATION 1.925700361 0.270329877 3.58107084
## PRODUCTIVITY-MAPS_AND_NAVIGATION -0.482462881 -2.071044916 1.10611915
## SHOPPING-MAPS_AND_NAVIGATION 1.189970525 -0.565308613 2.94524966
## SOCIAL-MAPS_AND_NAVIGATION 0.140822534 -1.560167115 1.84181218
## SPORTS-MAPS_AND_NAVIGATION -0.599651967 -2.219001126 1.01969719
## TOOLS-MAPS_AND_NAVIGATION -0.413704787 -1.885101423 1.05769185
## TRAVEL_AND_LOCAL-MAPS_AND_NAVIGATION 0.088172939 -1.640097588 1.81644347
## VIDEO_PLAYERS-MAPS_AND_NAVIGATION 1.221037050 -0.614992311 3.05706641
## WEATHER-MAPS_AND_NAVIGATION 1.591072134 -0.637854947 3.81999921
## NEWS_AND_MAGAZINES-MEDICAL 2.739304871 1.480836372 3.99777337
## PARENTING-MEDICAL 3.623782857 1.455744646 5.79182107
## PERSONALIZATION-MEDICAL 2.203910338 1.076530858 3.33128982
## PHOTOGRAPHY-MEDICAL 5.522953680 4.301837327 6.74407003
## PRODUCTIVITY-MEDICAL 3.114790438 1.985867680 4.24371320
## SHOPPING-MEDICAL 4.787223843 3.433754760 6.14069293
## SOCIAL-MEDICAL 3.738075852 2.455796829 5.02035487
## SPORTS-MEDICAL 2.997601351 1.825779946 4.16942276
## TOOLS-MEDICAL 3.183548531 2.226531411 4.14056565
## TRAVEL_AND_LOCAL-MEDICAL 3.685426258 2.367172593 5.00367992
## VIDEO_PLAYERS-MEDICAL 4.818290369 3.361623789 6.27495695
## WEATHER-MEDICAL 5.188325452 3.259857241 7.11679366
## PARENTING-NEWS_AND_MAGAZINES 0.884477986 -1.361511648 3.13046762
## PERSONALIZATION-NEWS_AND_MAGAZINES -0.535394534 -1.806246312 0.73545724
## PHOTOGRAPHY-NEWS_AND_MAGAZINES 2.783648809 1.428951463 4.13834615
## PRODUCTIVITY-NEWS_AND_MAGAZINES 0.375485567 -0.896735461 1.64770659
## SHOPPING-NEWS_AND_MAGAZINES 2.047918972 0.572805990 3.52303195
## SOCIAL-NEWS_AND_MAGAZINES 0.998770981 -0.411306762 2.40884872
## SPORTS-NEWS_AND_MAGAZINES 0.258296480 -1.052140529 1.56873349
## TOOLS-NEWS_AND_MAGAZINES 0.444243660 -0.678236415 1.56672374
## TRAVEL_AND_LOCAL-NEWS_AND_MAGAZINES 0.946121387 -0.496748141 2.38899091
## VIDEO_PLAYERS-NEWS_AND_MAGAZINES 2.078985498 0.508648822 3.64932217
## WEATHER-NEWS_AND_MAGAZINES 2.449020581 0.433314901 4.46472626
## PERSONALIZATION-PARENTING -1.419872519 -3.595122152 0.75537711
## PHOTOGRAPHY-PARENTING 1.899170823 -0.326104805 4.12444645
## PRODUCTIVITY-PARENTING -0.508992419 -2.685042295 1.66705746
## SHOPPING-PARENTING 1.163440986 -1.137125255 3.46400723
## SOCIAL-PARENTING 0.114292995 -2.145124178 2.37371017
## SPORTS-PARENTING -0.626181506 -2.824792857 1.57242985
## TOOLS-PARENTING -0.440234326 -2.532268800 1.65180015
## TRAVEL_AND_LOCAL-PARENTING 0.061643401 -2.218382738 2.34166954
## VIDEO_PLAYERS-PARENTING 1.194507512 -1.168245966 3.55726099
## WEATHER-PARENTING 1.564542595 -1.114956632 4.24404182
## PHOTOGRAPHY-PERSONALIZATION 3.319043342 2.085168784 4.55291790
## PRODUCTIVITY-PERSONALIZATION 0.910880100 -0.231830655 2.05359086
## SHOPPING-PERSONALIZATION 2.583313506 1.218322722 3.94830429
## SOCIAL-PERSONALIZATION 1.534165515 0.239730978 2.82860005
## SPORTS-PERSONALIZATION 0.793691014 -0.391419396 1.97880142
## TOOLS-PERSONALIZATION 0.979638194 0.006394623 1.95288176
## TRAVEL_AND_LOCAL-PERSONALIZATION 1.481515920 0.151435471 2.81159637
## VIDEO_PLAYERS-PERSONALIZATION 2.614380031 1.147001824 4.08175824
## WEATHER-PERSONALIZATION 2.984415115 1.047843165 4.92098706
## PRODUCTIVITY-PHOTOGRAPHY -2.408163242 -3.643448037 -1.17287845
## SHOPPING-PHOTOGRAPHY -0.735729836 -2.179107990 0.70764832
## SOCIAL-PHOTOGRAPHY -1.784877827 -3.161722563 -0.40803309
## SPORTS-PHOTOGRAPHY -2.525352328 -3.799961028 -1.25074363
## TOOLS-PHOTOGRAPHY -2.339405148 -3.419841959 -1.25896834
## TRAVEL_AND_LOCAL-PHOTOGRAPHY -1.837527422 -3.247936815 -0.42711803
## VIDEO_PLAYERS-PHOTOGRAPHY -0.704663311 -2.245227966 0.83590134
## WEATHER-PHOTOGRAPHY -0.334628227 -2.327227428 1.65797097
## SHOPPING-PRODUCTIVITY 1.672433405 0.306167714 3.03869910
## SOCIAL-PRODUCTIVITY 0.623285414 -0.672493453 1.91906428
## SPORTS-PRODUCTIVITY -0.117189087 -1.303767691 1.06938952
## TOOLS-PRODUCTIVITY 0.068758093 -0.906272751 1.04378894
## TRAVEL_AND_LOCAL-PRODUCTIVITY 0.570635820 -0.760752968 1.90202461
## VIDEO_PLAYERS-PRODUCTIVITY 1.703499931 0.234935699 3.17206416
## WEATHER-PRODUCTIVITY 2.073535014 0.136064235 4.01100579
## SOCIAL-SHOPPING -1.049147991 -2.544626122 0.44633014
## SPORTS-SHOPPING -1.789622492 -3.191542872 -0.38770211
## TOOLS-SHOPPING -1.603675312 -2.831721368 -0.37562926
## TRAVEL_AND_LOCAL-SHOPPING -1.101797586 -2.628233982 0.42463881
## VIDEO_PLAYERS-SHOPPING 0.031066526 -1.616383890 1.67851694
## WEATHER-SHOPPING 0.401101609 -1.675242531 2.47744575
## SPORTS-SOCIAL -0.740474501 -2.073794299 0.59284530
## TOOLS-SOCIAL -0.554527321 -1.703639173 0.59458453
## TRAVEL_AND_LOCAL-SOCIAL -0.052649594 -1.516332963 1.41103377
## VIDEO_PLAYERS-SOCIAL 1.080214517 -0.509267727 2.66969676
## WEATHER-SOCIAL 1.450249600 -0.580406924 3.48090612
## TOOLS-SPORTS 0.185947180 -0.838447257 1.21034162
## TRAVEL_AND_LOCAL-SPORTS 0.687824906 -0.680127913 2.05577773
## VIDEO_PLAYERS-SPORTS 1.820689018 0.318896849 3.32248119
## WEATHER-SPORTS 2.190724101 0.227947539 4.15350066
## TRAVEL_AND_LOCAL-TOOLS 0.501877726 -0.687244336 1.69099979
## VIDEO_PLAYERS-TOOLS 1.634741838 0.293810788 2.97567289
## WEATHER-TOOLS 2.004776921 0.162167848 3.84738599
## VIDEO_PLAYERS-TRAVEL_AND_LOCAL 1.132864111 -0.485779467 2.75150769
## WEATHER-TRAVEL_AND_LOCAL 1.502899195 -0.550663356 3.55646175
## WEATHER-VIDEO_PLAYERS 0.370035083 -1.775006630 2.51507680
## p adj
## AUTO_AND_VEHICLES-ART_AND_DESIGN 0.9905770
## BEAUTY-ART_AND_DESIGN 1.0000000
## BOOKS_AND_REFERENCE-ART_AND_DESIGN 0.7650853
## BUSINESS-ART_AND_DESIGN 0.0000002
## COMICS-ART_AND_DESIGN 1.0000000
## COMMUNICATION-ART_AND_DESIGN 1.0000000
## DATING-ART_AND_DESIGN 0.5288198
## EDUCATION-ART_AND_DESIGN 0.1681188
## ENTERTAINMENT-ART_AND_DESIGN 0.0000287
## EVENTS-ART_AND_DESIGN 0.0087638
## FAMILY-ART_AND_DESIGN 0.9998655
## FINANCE-ART_AND_DESIGN 0.9953429
## FOOD_AND_DRINK-ART_AND_DESIGN 1.0000000
## GAME-ART_AND_DESIGN 0.1044645
## HEALTH_AND_FITNESS-ART_AND_DESIGN 1.0000000
## HOUSE_AND_HOME-ART_AND_DESIGN 1.0000000
## LIBRARIES_AND_DEMO-ART_AND_DESIGN 0.9999327
## LIFESTYLE-ART_AND_DESIGN 0.3599194
## MAPS_AND_NAVIGATION-ART_AND_DESIGN 1.0000000
## MEDICAL-ART_AND_DESIGN 0.0000000
## NEWS_AND_MAGAZINES-ART_AND_DESIGN 0.9995685
## PARENTING-ART_AND_DESIGN 1.0000000
## PERSONALIZATION-ART_AND_DESIGN 0.7130524
## PHOTOGRAPHY-ART_AND_DESIGN 0.2657651
## PRODUCTIVITY-ART_AND_DESIGN 1.0000000
## SHOPPING-ART_AND_DESIGN 0.9954025
## SOCIAL-ART_AND_DESIGN 1.0000000
## SPORTS-ART_AND_DESIGN 0.9999994
## TOOLS-ART_AND_DESIGN 1.0000000
## TRAVEL_AND_LOCAL-ART_AND_DESIGN 1.0000000
## VIDEO_PLAYERS-ART_AND_DESIGN 0.9954212
## WEATHER-ART_AND_DESIGN 0.9595914
## BEAUTY-AUTO_AND_VEHICLES 1.0000000
## BOOKS_AND_REFERENCE-AUTO_AND_VEHICLES 1.0000000
## BUSINESS-AUTO_AND_VEHICLES 0.0061882
## COMICS-AUTO_AND_VEHICLES 0.9621172
## COMMUNICATION-AUTO_AND_VEHICLES 0.7147198
## DATING-AUTO_AND_VEHICLES 1.0000000
## EDUCATION-AUTO_AND_VEHICLES 0.0000011
## ENTERTAINMENT-AUTO_AND_VEHICLES 0.0000000
## EVENTS-AUTO_AND_VEHICLES 0.7596794
## FAMILY-AUTO_AND_VEHICLES 0.9999998
## FINANCE-AUTO_AND_VEHICLES 1.0000000
## FOOD_AND_DRINK-AUTO_AND_VEHICLES 0.7097936
## GAME-AUTO_AND_VEHICLES 0.0000000
## HEALTH_AND_FITNESS-AUTO_AND_VEHICLES 0.9899650
## HOUSE_AND_HOME-AUTO_AND_VEHICLES 0.5246592
## LIBRARIES_AND_DEMO-AUTO_AND_VEHICLES 1.0000000
## LIFESTYLE-AUTO_AND_VEHICLES 1.0000000
## MAPS_AND_NAVIGATION-AUTO_AND_VEHICLES 0.9589334
## MEDICAL-AUTO_AND_VEHICLES 0.0009049
## NEWS_AND_MAGAZINES-AUTO_AND_VEHICLES 1.0000000
## PARENTING-AUTO_AND_VEHICLES 0.9965941
## PERSONALIZATION-AUTO_AND_VEHICLES 1.0000000
## PHOTOGRAPHY-AUTO_AND_VEHICLES 0.0000003
## PRODUCTIVITY-AUTO_AND_VEHICLES 0.9998582
## SHOPPING-AUTO_AND_VEHICLES 0.0021874
## SOCIAL-AUTO_AND_VEHICLES 0.7003399
## SPORTS-AUTO_AND_VEHICLES 0.9999973
## TOOLS-AUTO_AND_VEHICLES 0.9980023
## TRAVEL_AND_LOCAL-AUTO_AND_VEHICLES 0.7962716
## VIDEO_PLAYERS-AUTO_AND_VEHICLES 0.0033886
## WEATHER-AUTO_AND_VEHICLES 0.0046025
## BOOKS_AND_REFERENCE-BEAUTY 0.9999996
## BUSINESS-BEAUTY 0.0030178
## COMICS-BEAUTY 0.9999995
## COMMUNICATION-BEAUTY 0.9999991
## DATING-BEAUTY 0.9999057
## EDUCATION-BEAUTY 0.0071951
## ENTERTAINMENT-BEAUTY 0.0000003
## EVENTS-BEAUTY 0.3761557
## FAMILY-BEAUTY 1.0000000
## FINANCE-BEAUTY 1.0000000
## FOOD_AND_DRINK-BEAUTY 0.9999638
## GAME-BEAUTY 0.0023255
## HEALTH_AND_FITNESS-BEAUTY 1.0000000
## HOUSE_AND_HOME-BEAUTY 0.9982507
## LIBRARIES_AND_DEMO-BEAUTY 1.0000000
## LIFESTYLE-BEAUTY 0.9997246
## MAPS_AND_NAVIGATION-BEAUTY 1.0000000
## MEDICAL-BEAUTY 0.0005851
## NEWS_AND_MAGAZINES-BEAUTY 1.0000000
## PARENTING-BEAUTY 1.0000000
## PERSONALIZATION-BEAUTY 0.9999996
## PHOTOGRAPHY-BEAUTY 0.0108336
## PRODUCTIVITY-BEAUTY 1.0000000
## SHOPPING-BEAUTY 0.4900368
## SOCIAL-BEAUTY 0.9999972
## SPORTS-BEAUTY 1.0000000
## TOOLS-BEAUTY 1.0000000
## TRAVEL_AND_LOCAL-BEAUTY 0.9999995
## VIDEO_PLAYERS-BEAUTY 0.5087479
## WEATHER-BEAUTY 0.3585261
## BUSINESS-BOOKS_AND_REFERENCE 0.0000062
## COMICS-BOOKS_AND_REFERENCE 0.6153117
## COMMUNICATION-BOOKS_AND_REFERENCE 0.0116424
## DATING-BOOKS_AND_REFERENCE 1.0000000
## EDUCATION-BOOKS_AND_REFERENCE 0.0000000
## ENTERTAINMENT-BOOKS_AND_REFERENCE 0.0000000
## EVENTS-BOOKS_AND_REFERENCE 0.6598727
## FAMILY-BOOKS_AND_REFERENCE 0.8791930
## FINANCE-BOOKS_AND_REFERENCE 0.9999968
## FOOD_AND_DRINK-BOOKS_AND_REFERENCE 0.0766260
## GAME-BOOKS_AND_REFERENCE 0.0000000
## HEALTH_AND_FITNESS-BOOKS_AND_REFERENCE 0.2849977
## HOUSE_AND_HOME-BOOKS_AND_REFERENCE 0.0620317
## LIBRARIES_AND_DEMO-BOOKS_AND_REFERENCE 1.0000000
## LIFESTYLE-BOOKS_AND_REFERENCE 1.0000000
## MAPS_AND_NAVIGATION-BOOKS_AND_REFERENCE 0.3224421
## MEDICAL-BOOKS_AND_REFERENCE 0.0000002
## NEWS_AND_MAGAZINES-BOOKS_AND_REFERENCE 0.9999271
## PARENTING-BOOKS_AND_REFERENCE 0.8665016
## PERSONALIZATION-BOOKS_AND_REFERENCE 1.0000000
## PHOTOGRAPHY-BOOKS_AND_REFERENCE 0.0000000
## PRODUCTIVITY-BOOKS_AND_REFERENCE 0.6761301
## SHOPPING-BOOKS_AND_REFERENCE 0.0000000
## SOCIAL-BOOKS_AND_REFERENCE 0.0179804
## SPORTS-BOOKS_AND_REFERENCE 0.9208618
## TOOLS-BOOKS_AND_REFERENCE 0.2515531
## TRAVEL_AND_LOCAL-BOOKS_AND_REFERENCE 0.0407043
## VIDEO_PLAYERS-BOOKS_AND_REFERENCE 0.0000003
## WEATHER-BOOKS_AND_REFERENCE 0.0000123
## COMICS-BUSINESS 0.0000002
## COMMUNICATION-BUSINESS 0.0000000
## DATING-BUSINESS 0.0018729
## EDUCATION-BUSINESS 0.0000000
## ENTERTAINMENT-BUSINESS 0.0000000
## EVENTS-BUSINESS 1.0000000
## FAMILY-BUSINESS 0.0000000
## FINANCE-BUSINESS 0.0000000
## FOOD_AND_DRINK-BUSINESS 0.0000000
## GAME-BUSINESS 0.0000000
## HEALTH_AND_FITNESS-BUSINESS 0.0000000
## HOUSE_AND_HOME-BUSINESS 0.0000000
## LIBRARIES_AND_DEMO-BUSINESS 0.0003603
## LIFESTYLE-BUSINESS 0.0000018
## MAPS_AND_NAVIGATION-BUSINESS 0.0000000
## MEDICAL-BUSINESS 1.0000000
## NEWS_AND_MAGAZINES-BUSINESS 0.0000000
## PARENTING-BUSINESS 0.0000012
## PERSONALIZATION-BUSINESS 0.0000000
## PHOTOGRAPHY-BUSINESS 0.0000000
## PRODUCTIVITY-BUSINESS 0.0000000
## SHOPPING-BUSINESS 0.0000000
## SOCIAL-BUSINESS 0.0000000
## SPORTS-BUSINESS 0.0000000
## TOOLS-BUSINESS 0.0000000
## TRAVEL_AND_LOCAL-BUSINESS 0.0000000
## VIDEO_PLAYERS-BUSINESS 0.0000000
## WEATHER-BUSINESS 0.0000000
## COMMUNICATION-COMICS 1.0000000
## DATING-COMICS 0.3865153
## EDUCATION-COMICS 0.4614186
## ENTERTAINMENT-COMICS 0.0004270
## EVENTS-COMICS 0.0052979
## FAMILY-COMICS 0.9974780
## FINANCE-COMICS 0.9735980
## FOOD_AND_DRINK-COMICS 1.0000000
## GAME-COMICS 0.4272084
## HEALTH_AND_FITNESS-COMICS 1.0000000
## HOUSE_AND_HOME-COMICS 1.0000000
## LIBRARIES_AND_DEMO-COMICS 0.9989513
## LIFESTYLE-COMICS 0.2487601
## MAPS_AND_NAVIGATION-COMICS 1.0000000
## MEDICAL-COMICS 0.0000000
## NEWS_AND_MAGAZINES-COMICS 0.9950291
## PARENTING-COMICS 1.0000000
## PERSONALIZATION-COMICS 0.5581835
## PHOTOGRAPHY-COMICS 0.6589917
## PRODUCTIVITY-COMICS 0.9999970
## SHOPPING-COMICS 0.9999610
## SOCIAL-COMICS 1.0000000
## SPORTS-COMICS 0.9999416
## TOOLS-COMICS 0.9999992
## TRAVEL_AND_LOCAL-COMICS 1.0000000
## VIDEO_PLAYERS-COMICS 0.9999533
## WEATHER-COMICS 0.9971709
## DATING-COMMUNICATION 0.0039840
## EDUCATION-COMMUNICATION 0.0004714
## ENTERTAINMENT-COMMUNICATION 0.0000000
## EVENTS-COMMUNICATION 0.0000211
## FAMILY-COMMUNICATION 0.2663033
## FINANCE-COMMUNICATION 0.2375070
## FOOD_AND_DRINK-COMMUNICATION 1.0000000
## GAME-COMMUNICATION 0.0000000
## HEALTH_AND_FITNESS-COMMUNICATION 1.0000000
## HOUSE_AND_HOME-COMMUNICATION 1.0000000
## LIBRARIES_AND_DEMO-COMMUNICATION 0.9848282
## LIFESTYLE-COMMUNICATION 0.0000258
## MAPS_AND_NAVIGATION-COMMUNICATION 1.0000000
## MEDICAL-COMMUNICATION 0.0000000
## NEWS_AND_MAGAZINES-COMMUNICATION 0.6613765
## PARENTING-COMMUNICATION 1.0000000
## PERSONALIZATION-COMMUNICATION 0.0012258
## PHOTOGRAPHY-COMMUNICATION 0.0000283
## PRODUCTIVITY-COMMUNICATION 0.9973931
## SHOPPING-COMMUNICATION 0.4519509
## SOCIAL-COMMUNICATION 1.0000000
## SPORTS-COMMUNICATION 0.9728222
## TOOLS-COMMUNICATION 0.9966165
## TRAVEL_AND_LOCAL-COMMUNICATION 1.0000000
## VIDEO_PLAYERS-COMMUNICATION 0.5496141
## WEATHER-COMMUNICATION 0.5088768
## EDUCATION-DATING 0.0000000
## ENTERTAINMENT-DATING 0.0000000
## EVENTS-DATING 0.9358509
## FAMILY-DATING 0.5783899
## FINANCE-DATING 0.9978471
## FOOD_AND_DRINK-DATING 0.0289571
## GAME-DATING 0.0000000
## HEALTH_AND_FITNESS-DATING 0.1191131
## HOUSE_AND_HOME-DATING 0.0243873
## LIBRARIES_AND_DEMO-DATING 0.9999966
## LIFESTYLE-DATING 1.0000000
## MAPS_AND_NAVIGATION-DATING 0.1469049
## MEDICAL-DATING 0.0001288
## NEWS_AND_MAGAZINES-DATING 0.9911170
## PARENTING-DATING 0.6644251
## PERSONALIZATION-DATING 1.0000000
## PHOTOGRAPHY-DATING 0.0000000
## PRODUCTIVITY-DATING 0.3693932
## SHOPPING-DATING 0.0000000
## SOCIAL-DATING 0.0060913
## SPORTS-DATING 0.6735607
## TOOLS-DATING 0.1019151
## TRAVEL_AND_LOCAL-DATING 0.0141499
## VIDEO_PLAYERS-DATING 0.0000001
## WEATHER-DATING 0.0000039
## ENTERTAINMENT-EDUCATION 0.8131444
## EVENTS-EDUCATION 0.0000000
## FAMILY-EDUCATION 0.0000000
## FINANCE-EDUCATION 0.0000000
## FOOD_AND_DRINK-EDUCATION 0.1064637
## GAME-EDUCATION 1.0000000
## HEALTH_AND_FITNESS-EDUCATION 0.0000122
## HOUSE_AND_HOME-EDUCATION 0.7113674
## LIBRARIES_AND_DEMO-EDUCATION 0.0000278
## LIFESTYLE-EDUCATION 0.0000000
## MAPS_AND_NAVIGATION-EDUCATION 0.0064487
## MEDICAL-EDUCATION 0.0000000
## NEWS_AND_MAGAZINES-EDUCATION 0.0000000
## PARENTING-EDUCATION 0.1597553
## PERSONALIZATION-EDUCATION 0.0000000
## PHOTOGRAPHY-EDUCATION 1.0000000
## PRODUCTIVITY-EDUCATION 0.0000001
## SHOPPING-EDUCATION 0.9394882
## SOCIAL-EDUCATION 0.0021257
## SPORTS-EDUCATION 0.0000001
## TOOLS-EDUCATION 0.0000000
## TRAVEL_AND_LOCAL-EDUCATION 0.0017366
## VIDEO_PLAYERS-EDUCATION 0.9754629
## WEATHER-EDUCATION 0.9999999
## EVENTS-ENTERTAINMENT 0.0000000
## FAMILY-ENTERTAINMENT 0.0000000
## FINANCE-ENTERTAINMENT 0.0000000
## FOOD_AND_DRINK-ENTERTAINMENT 0.0000019
## GAME-ENTERTAINMENT 0.0351154
## HEALTH_AND_FITNESS-ENTERTAINMENT 0.0000000
## HOUSE_AND_HOME-ENTERTAINMENT 0.0007895
## LIBRARIES_AND_DEMO-ENTERTAINMENT 0.0000000
## LIFESTYLE-ENTERTAINMENT 0.0000000
## MAPS_AND_NAVIGATION-ENTERTAINMENT 0.0000000
## MEDICAL-ENTERTAINMENT 0.0000000
## NEWS_AND_MAGAZINES-ENTERTAINMENT 0.0000000
## PARENTING-ENTERTAINMENT 0.0000321
## PERSONALIZATION-ENTERTAINMENT 0.0000000
## PHOTOGRAPHY-ENTERTAINMENT 0.0853659
## PRODUCTIVITY-ENTERTAINMENT 0.0000000
## SHOPPING-ENTERTAINMENT 0.0004107
## SOCIAL-ENTERTAINMENT 0.0000000
## SPORTS-ENTERTAINMENT 0.0000000
## TOOLS-ENTERTAINMENT 0.0000000
## TRAVEL_AND_LOCAL-ENTERTAINMENT 0.0000000
## VIDEO_PLAYERS-ENTERTAINMENT 0.0013470
## WEATHER-ENTERTAINMENT 0.1968678
## FAMILY-EVENTS 0.0053488
## FINANCE-EVENTS 0.0790048
## FOOD_AND_DRINK-EVENTS 0.0001158
## GAME-EVENTS 0.0000000
## HEALTH_AND_FITNESS-EVENTS 0.0005831
## HOUSE_AND_HOME-EVENTS 0.0001042
## LIBRARIES_AND_DEMO-EVENTS 0.3938637
## LIFESTYLE-EVENTS 0.8392205
## MAPS_AND_NAVIGATION-EVENTS 0.0007756
## MEDICAL-EVENTS 1.0000000
## NEWS_AND_MAGAZINES-EVENTS 0.0598395
## PARENTING-EVENTS 0.0159190
## PERSONALIZATION-EVENTS 0.4999117
## PHOTOGRAPHY-EVENTS 0.0000000
## PRODUCTIVITY-EVENTS 0.0025341
## SHOPPING-EVENTS 0.0000000
## SOCIAL-EVENTS 0.0000276
## SPORTS-EVENTS 0.0077265
## TOOLS-EVENTS 0.0005574
## TRAVEL_AND_LOCAL-EVENTS 0.0000598
## VIDEO_PLAYERS-EVENTS 0.0000000
## WEATHER-EVENTS 0.0000000
## FINANCE-FAMILY 1.0000000
## FOOD_AND_DRINK-FAMILY 0.7396645
## GAME-FAMILY 0.0000000
## HEALTH_AND_FITNESS-FAMILY 0.9971968
## HOUSE_AND_HOME-FAMILY 0.6024533
## LIBRARIES_AND_DEMO-FAMILY 1.0000000
## LIFESTYLE-FAMILY 0.0364395
## MAPS_AND_NAVIGATION-FAMILY 0.9916099
## MEDICAL-FAMILY 0.0000000
## NEWS_AND_MAGAZINES-FAMILY 1.0000000
## PARENTING-FAMILY 0.9999864
## PERSONALIZATION-FAMILY 0.5338795
## PHOTOGRAPHY-FAMILY 0.0000000
## PRODUCTIVITY-FAMILY 1.0000000
## SHOPPING-FAMILY 0.0000002
## SOCIAL-FAMILY 0.3886807
## SPORTS-FAMILY 1.0000000
## TOOLS-FAMILY 0.9976804
## TRAVEL_AND_LOCAL-FAMILY 0.6318131
## VIDEO_PLAYERS-FAMILY 0.0000042
## WEATHER-FAMILY 0.0005028
## FOOD_AND_DRINK-FINANCE 0.5268048
## GAME-FINANCE 0.0000000
## HEALTH_AND_FITNESS-FINANCE 0.9599754
## HOUSE_AND_HOME-FINANCE 0.3982222
## LIBRARIES_AND_DEMO-FINANCE 1.0000000
## LIFESTYLE-FINANCE 0.9570430
## MAPS_AND_NAVIGATION-FINANCE 0.9289711
## MEDICAL-FINANCE 0.0000000
## NEWS_AND_MAGAZINES-FINANCE 1.0000000
## PARENTING-FINANCE 0.9989280
## PERSONALIZATION-FINANCE 0.9999836
## PHOTOGRAPHY-FINANCE 0.0000000
## PRODUCTIVITY-FINANCE 0.9998231
## SHOPPING-FINANCE 0.0000020
## SOCIAL-FINANCE 0.2913978
## SPORTS-FINANCE 0.9999999
## TOOLS-FINANCE 0.9767887
## TRAVEL_AND_LOCAL-FINANCE 0.4646598
## VIDEO_PLAYERS-FINANCE 0.0000129
## WEATHER-FINANCE 0.0003335
## GAME-FOOD_AND_DRINK 0.0217208
## HEALTH_AND_FITNESS-FOOD_AND_DRINK 0.9999986
## HOUSE_AND_HOME-FOOD_AND_DRINK 1.0000000
## LIBRARIES_AND_DEMO-FOOD_AND_DRINK 0.9701107
## LIFESTYLE-FOOD_AND_DRINK 0.0044235
## MAPS_AND_NAVIGATION-FOOD_AND_DRINK 1.0000000
## MEDICAL-FOOD_AND_DRINK 0.0000000
## NEWS_AND_MAGAZINES-FOOD_AND_DRINK 0.7987142
## PARENTING-FOOD_AND_DRINK 1.0000000
## PERSONALIZATION-FOOD_AND_DRINK 0.0377018
## PHOTOGRAPHY-FOOD_AND_DRINK 0.1391968
## PRODUCTIVITY-FOOD_AND_DRINK 0.9969458
## SHOPPING-FOOD_AND_DRINK 0.9980216
## SOCIAL-FOOD_AND_DRINK 1.0000000
## SPORTS-FOOD_AND_DRINK 0.9810361
## TOOLS-FOOD_AND_DRINK 0.9978802
## TRAVEL_AND_LOCAL-FOOD_AND_DRINK 1.0000000
## VIDEO_PLAYERS-FOOD_AND_DRINK 0.9982062
## WEATHER-FOOD_AND_DRINK 0.9759116
## HEALTH_AND_FITNESS-GAME 0.0000000
## HOUSE_AND_HOME-GAME 0.6729496
## LIBRARIES_AND_DEMO-GAME 0.0000003
## LIFESTYLE-GAME 0.0000000
## MAPS_AND_NAVIGATION-GAME 0.0001202
## MEDICAL-GAME 0.0000000
## NEWS_AND_MAGAZINES-GAME 0.0000000
## PARENTING-GAME 0.1042735
## PERSONALIZATION-GAME 0.0000000
## PHOTOGRAPHY-GAME 1.0000000
## PRODUCTIVITY-GAME 0.0000000
## SHOPPING-GAME 0.8274017
## SOCIAL-GAME 0.0000003
## SPORTS-GAME 0.0000000
## TOOLS-GAME 0.0000000
## TRAVEL_AND_LOCAL-GAME 0.0000004
## VIDEO_PLAYERS-GAME 0.9563801
## WEATHER-GAME 1.0000000
## HOUSE_AND_HOME-HEALTH_AND_FITNESS 0.9994599
## LIBRARIES_AND_DEMO-HEALTH_AND_FITNESS 0.9999936
## LIFESTYLE-HEALTH_AND_FITNESS 0.0078511
## MAPS_AND_NAVIGATION-HEALTH_AND_FITNESS 1.0000000
## MEDICAL-HEALTH_AND_FITNESS 0.0000000
## NEWS_AND_MAGAZINES-HEALTH_AND_FITNESS 0.9989587
## PARENTING-HEALTH_AND_FITNESS 1.0000000
## PERSONALIZATION-HEALTH_AND_FITNESS 0.1125977
## PHOTOGRAPHY-HEALTH_AND_FITNESS 0.0000002
## PRODUCTIVITY-HEALTH_AND_FITNESS 1.0000000
## SHOPPING-HEALTH_AND_FITNESS 0.0484269
## SOCIAL-HEALTH_AND_FITNESS 1.0000000
## SPORTS-HEALTH_AND_FITNESS 1.0000000
## TOOLS-HEALTH_AND_FITNESS 1.0000000
## TRAVEL_AND_LOCAL-HEALTH_AND_FITNESS 1.0000000
## VIDEO_PLAYERS-HEALTH_AND_FITNESS 0.0836878
## WEATHER-HEALTH_AND_FITNESS 0.1222167
## LIBRARIES_AND_DEMO-HOUSE_AND_HOME 0.8787444
## LIFESTYLE-HOUSE_AND_HOME 0.0062336
## MAPS_AND_NAVIGATION-HOUSE_AND_HOME 1.0000000
## MEDICAL-HOUSE_AND_HOME 0.0000000
## NEWS_AND_MAGAZINES-HOUSE_AND_HOME 0.6346359
## PARENTING-HOUSE_AND_HOME 1.0000000
## PERSONALIZATION-HOUSE_AND_HOME 0.0374836
## PHOTOGRAPHY-HOUSE_AND_HOME 0.8832210
## PRODUCTIVITY-HOUSE_AND_HOME 0.9665871
## SHOPPING-HOUSE_AND_HOME 1.0000000
## SOCIAL-HOUSE_AND_HOME 1.0000000
## SPORTS-HOUSE_AND_HOME 0.9073393
## TOOLS-HOUSE_AND_HOME 0.9728316
## TRAVEL_AND_LOCAL-HOUSE_AND_HOME 1.0000000
## VIDEO_PLAYERS-HOUSE_AND_HOME 1.0000000
## WEATHER-HOUSE_AND_HOME 0.9999745
## LIFESTYLE-LIBRARIES_AND_DEMO 0.9999805
## MAPS_AND_NAVIGATION-LIBRARIES_AND_DEMO 0.9996290
## MEDICAL-LIBRARIES_AND_DEMO 0.0000398
## NEWS_AND_MAGAZINES-LIBRARIES_AND_DEMO 1.0000000
## PARENTING-LIBRARIES_AND_DEMO 0.9999877
## PERSONALIZATION-LIBRARIES_AND_DEMO 1.0000000
## PHOTOGRAPHY-LIBRARIES_AND_DEMO 0.0000125
## PRODUCTIVITY-LIBRARIES_AND_DEMO 1.0000000
## SHOPPING-LIBRARIES_AND_DEMO 0.0267194
## SOCIAL-LIBRARIES_AND_DEMO 0.9801305
## SPORTS-LIBRARIES_AND_DEMO 1.0000000
## TOOLS-LIBRARIES_AND_DEMO 0.9999999
## TRAVEL_AND_LOCAL-LIBRARIES_AND_DEMO 0.9919899
## VIDEO_PLAYERS-LIBRARIES_AND_DEMO 0.0353235
## WEATHER-LIBRARIES_AND_DEMO 0.0333740
## MAPS_AND_NAVIGATION-LIFESTYLE 0.0339397
## MEDICAL-LIFESTYLE 0.0000000
## NEWS_AND_MAGAZINES-LIFESTYLE 0.9133558
## PARENTING-LIFESTYLE 0.5089691
## PERSONALIZATION-LIFESTYLE 1.0000000
## PHOTOGRAPHY-LIFESTYLE 0.0000000
## PRODUCTIVITY-LIFESTYLE 0.0461900
## SHOPPING-LIFESTYLE 0.0000000
## SOCIAL-LIFESTYLE 0.0001038
## SPORTS-LIFESTYLE 0.2151106
## TOOLS-LIFESTYLE 0.0010087
## TRAVEL_AND_LOCAL-LIFESTYLE 0.0004523
## VIDEO_PLAYERS-LIFESTYLE 0.0000000
## WEATHER-LIFESTYLE 0.0000001
## MEDICAL-MAPS_AND_NAVIGATION 0.0000000
## NEWS_AND_MAGAZINES-MAPS_AND_NAVIGATION 0.9919776
## PARENTING-MAPS_AND_NAVIGATION 1.0000000
## PERSONALIZATION-MAPS_AND_NAVIGATION 0.2033549
## PHOTOGRAPHY-MAPS_AND_NAVIGATION 0.0044525
## PRODUCTIVITY-MAPS_AND_NAVIGATION 0.9999998
## SHOPPING-MAPS_AND_NAVIGATION 0.7718214
## SOCIAL-MAPS_AND_NAVIGATION 1.0000000
## SPORTS-MAPS_AND_NAVIGATION 0.9999816
## TOOLS-MAPS_AND_NAVIGATION 1.0000000
## TRAVEL_AND_LOCAL-MAPS_AND_NAVIGATION 1.0000000
## VIDEO_PLAYERS-MAPS_AND_NAVIGATION 0.8050502
## WEATHER-MAPS_AND_NAVIGATION 0.6680247
## NEWS_AND_MAGAZINES-MEDICAL 0.0000000
## PARENTING-MEDICAL 0.0000001
## PERSONALIZATION-MEDICAL 0.0000000
## PHOTOGRAPHY-MEDICAL 0.0000000
## PRODUCTIVITY-MEDICAL 0.0000000
## SHOPPING-MEDICAL 0.0000000
## SOCIAL-MEDICAL 0.0000000
## SPORTS-MEDICAL 0.0000000
## TOOLS-MEDICAL 0.0000000
## TRAVEL_AND_LOCAL-MEDICAL 0.0000000
## VIDEO_PLAYERS-MEDICAL 0.0000000
## WEATHER-MEDICAL 0.0000000
## PARENTING-NEWS_AND_MAGAZINES 0.9999303
## PERSONALIZATION-NEWS_AND_MAGAZINES 0.9997235
## PHOTOGRAPHY-NEWS_AND_MAGAZINES 0.0000000
## PRODUCTIVITY-NEWS_AND_MAGAZINES 0.9999999
## SHOPPING-NEWS_AND_MAGAZINES 0.0000701
## SOCIAL-NEWS_AND_MAGAZINES 0.6848545
## SPORTS-NEWS_AND_MAGAZINES 1.0000000
## TOOLS-NEWS_AND_MAGAZINES 0.9999226
## TRAVEL_AND_LOCAL-NEWS_AND_MAGAZINES 0.8274253
## VIDEO_PLAYERS-NEWS_AND_MAGAZINES 0.0002508
## WEATHER-NEWS_AND_MAGAZINES 0.0018549
## PERSONALIZATION-PARENTING 0.8342765
## PHOTOGRAPHY-PARENTING 0.2557528
## PRODUCTIVITY-PARENTING 1.0000000
## SHOPPING-PARENTING 0.9929068
## SOCIAL-PARENTING 1.0000000
## SPORTS-PARENTING 1.0000000
## TOOLS-PARENTING 1.0000000
## TRAVEL_AND_LOCAL-PARENTING 1.0000000
## VIDEO_PLAYERS-PARENTING 0.9929422
## WEATHER-PARENTING 0.9482818
## PHOTOGRAPHY-PERSONALIZATION 0.0000000
## PRODUCTIVITY-PERSONALIZATION 0.4064198
## SHOPPING-PERSONALIZATION 0.0000000
## SOCIAL-PERSONALIZATION 0.0030906
## SPORTS-PERSONALIZATION 0.7932928
## TOOLS-PERSONALIZATION 0.0458761
## TRAVEL_AND_LOCAL-PERSONALIZATION 0.0098178
## VIDEO_PLAYERS-PERSONALIZATION 0.0000000
## WEATHER-PERSONALIZATION 0.0000026
## PRODUCTIVITY-PHOTOGRAPHY 0.0000000
## SHOPPING-PHOTOGRAPHY 0.9919803
## SOCIAL-PHOTOGRAPHY 0.0004241
## SPORTS-PHOTOGRAPHY 0.0000000
## TOOLS-PHOTOGRAPHY 0.0000000
## TRAVEL_AND_LOCAL-PHOTOGRAPHY 0.0003752
## VIDEO_PLAYERS-PHOTOGRAPHY 0.9986926
## WEATHER-PHOTOGRAPHY 1.0000000
## SHOPPING-PRODUCTIVITY 0.0015812
## SOCIAL-PRODUCTIVITY 0.9968572
## SPORTS-PRODUCTIVITY 1.0000000
## TOOLS-PRODUCTIVITY 1.0000000
## TRAVEL_AND_LOCAL-PRODUCTIVITY 0.9996128
## VIDEO_PLAYERS-PRODUCTIVITY 0.0047029
## WEATHER-PRODUCTIVITY 0.0189358
## SOCIAL-SHOPPING 0.7051079
## SPORTS-SHOPPING 0.0006137
## TOOLS-SHOPPING 0.0003542
## TRAVEL_AND_LOCAL-SHOPPING 0.6432888
## VIDEO_PLAYERS-SHOPPING 1.0000000
## WEATHER-SHOPPING 1.0000000
## SPORTS-SOCIAL 0.9725029
## TOOLS-SOCIAL 0.9966816
## TRAVEL_AND_LOCAL-SOCIAL 1.0000000
## VIDEO_PLAYERS-SOCIAL 0.7673559
## WEATHER-SOCIAL 0.6669524
## TOOLS-SPORTS 1.0000000
## TRAVEL_AND_LOCAL-SPORTS 0.9935210
## VIDEO_PLAYERS-SPORTS 0.0019416
## WEATHER-SPORTS 0.0094762
## TRAVEL_AND_LOCAL-TOOLS 0.9997134
## VIDEO_PLAYERS-TOOLS 0.0017256
## WEATHER-TOOLS 0.0145571
## VIDEO_PLAYERS-TRAVEL_AND_LOCAL 0.7100174
## WEATHER-TRAVEL_AND_LOCAL 0.6116588
## WEATHER-VIDEO_PLAYERS 1.0000000Observations: - Installs for the Business category are significantly lower than those for Art and Design. - installs for the Entertainment category being higher than those for Art and Design. - Medical Category have lower Installs compared to Art and Design. - Installs in the Shopping category being higher than in Auto and Vehicles. - Installs for Game are significantly higher than those for Beauty. Many other comparisions do not have significance bwteen the categories as they have p value greater than 0.05.
Android version with mean(Installs)
# Ensure that Android.Ver is treated as a factor
data_final$Android.Ver <- as.factor(data_final$Android.Ver)
# Perform one-way ANOVA
anova_result <- aov(Installs ~ Android.Ver, data = data_final)
# Summary of the ANOVA result
anova_summary <- summary(anova_result)
print(anova_summary)## Df Sum Sq Mean Sq F value Pr(>F)
## Android.Ver 33 1.143e+18 3.463e+16 12.45 <2e-16 ***
## Residuals 9625 2.677e+19 2.781e+15
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The ANOVA results above indicate that there are significant differences among the group means for Android.Ver.
# As ANOVA is significant, performing a post-hoc test
if (anova_summary[[1]][["Pr(>F)"]][1] < 0.05) {
posthoc_result <- TukeyHSD(anova_result)
print(posthoc_result)
}## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Installs ~ Android.Ver, data = data_final)
##
## $Android.Ver
## diff lwr upr p adj
## 1.5 and up-1.0 and up 1162085.500 -147882419 150206590 1.0000000
## 1.6 and up-1.0 and up 370117.690 -142958078 143698313 1.0000000
## 2.0 and up-1.0 and up 1079778.438 -145402165 147561722 1.0000000
## 2.0.1 and up-1.0 and up 14408580.000 -146727153 175544313 1.0000000
## 2.1 and up-1.0 and up 2342340.278 -140830516 145515196 1.0000000
## 2.2 - 7.1.1-1.0 and up -29900.000 -246168798 246108998 1.0000000
## 2.2 and up-1.0 and up 375695.544 -142326020 143077412 1.0000000
## 2.3 and up-1.0 and up 2451520.145 -139887347 144790388 1.0000000
## 2.3.3 and up-1.0 and up 2551694.194 -140076258 145179647 1.0000000
## 3.0 and up-1.0 and up 1795152.126 -140927069 144517373 1.0000000
## 3.1 and up-1.0 and up 5073700.500 -150598207 160745608 1.0000000
## 3.2 and up-1.0 and up 200714.583 -145801745 146203174 1.0000000
## 4.0 and up-1.0 and up 4448261.639 -137770645 146667168 1.0000000
## 4.0.3 - 7.1.1-1.0 and up 7470000.000 -193501569 208441569 1.0000000
## 4.0.3 and up-1.0 and up 3638445.651 -138571747 145848638 1.0000000
## 4.1 - 7.1.1-1.0 and up 99970000.000 -146168898 346108898 0.9998945
## 4.1 and up-1.0 and up 5791588.460 -136381292 147964469 1.0000000
## 4.2 and up-1.0 and up 3635356.597 -138854502 146125215 1.0000000
## 4.3 and up-1.0 and up 2545998.738 -140203936 145295934 1.0000000
## 4.4 and up-1.0 and up 6012273.225 -136269706 148294253 1.0000000
## 4.4W and up-1.0 and up -27520.909 -154515595 154460553 1.0000000
## 5.0 - 6.0-1.0 and up -20000.000 -246158898 246118898 1.0000000
## 5.0 - 7.1.1-1.0 and up -29995.000 -246168893 246108903 1.0000000
## 5.0 - 8.0-1.0 and up 9970000.000 -191001569 210941569 1.0000000
## 5.0 and up-1.0 and up 3137590.514 -139248053 145523234 1.0000000
## 5.1 and up-1.0 and up 261898.182 -148165442 148689238 1.0000000
## 6.0 and up-1.0 and up 944933.167 -143771136 145661003 1.0000000
## 7.0 - 7.1.1-1.0 and up 970000.000 -245168898 247108898 1.0000000
## 7.0 and up-1.0 and up 5291657.143 -140160886 150744200 1.0000000
## 7.1 and up-1.0 and up 33653333.333 -149807769 217114436 1.0000000
## 8.0 and up-1.0 and up 221684.333 -163870914 164314283 1.0000000
## NaN-1.0 and up -24500.000 -200996069 200947069 1.0000000
## Varies with device-1.0 and up 39444362.406 -102807468 181696193 1.0000000
## 1.6 and up-1.5 and up -791967.810 -49450621 47866685 1.0000000
## 2.0 and up-1.5 and up -82307.063 -57368018 57203404 1.0000000
## 2.0.1 and up-1.5 and up 13246494.500 -75011181 101504170 1.0000000
## 2.1 and up-1.5 and up 1180254.778 -47018911 49379420 1.0000000
## 2.2 - 7.1.1-1.5 and up -1191985.500 -207126563 204742592 1.0000000
## 2.2 and up-1.5 and up -786389.956 -47567504 45994724 1.0000000
## 2.3 and up-1.5 and up 1289434.644 -44372870 46951739 1.0000000
## 2.3.3 and up-1.5 and up 1389608.694 -45166011 47945228 1.0000000
## 3.0 and up-1.5 and up 633066.626 -46210558 47476692 1.0000000
## 3.1 and up-1.5 and up 3911615.000 -73924339 81747569 1.0000000
## 3.2 and up-1.5 and up -961370.917 -57009664 55086922 1.0000000
## 4.0 and up-1.5 and up 3286176.139 -42000799 48573152 1.0000000
## 4.0.3 - 7.1.1-1.5 and up 6307914.500 -142736590 155352419 1.0000000
## 4.0.3 and up-1.5 and up 2476360.151 -42783243 47735963 1.0000000
## 4.1 - 7.1.1-1.5 and up 98807914.500 -107126663 304742492 0.9973799
## 4.1 and up-1.5 and up 4629502.960 -40512726 49771731 1.0000000
## 4.2 and up-1.5 and up 2473271.097 -43657550 48604093 1.0000000
## 4.3 and up-1.5 and up 1383913.238 -45544083 48311909 1.0000000
## 4.4 and up-1.5 and up 4850187.725 -40634475 50334851 1.0000000
## 4.4W and up-1.5 and up -1189606.409 -76630032 74250819 1.0000000
## 5.0 - 6.0-1.5 and up -1182085.500 -207116663 204752492 1.0000000
## 5.0 - 7.1.1-1.5 and up -1192080.500 -207126658 204742497 1.0000000
## 5.0 - 8.0-1.5 and up 8807914.500 -140236590 157852419 1.0000000
## 5.0 and up-1.5 and up 1975505.014 -43832403 47783413 1.0000000
## 5.1 and up-1.5 and up -900187.318 -62991799 61191424 1.0000000
## 6.0 and up-1.5 and up -217152.333 -52823555 52389250 1.0000000
## 7.0 - 7.1.1-1.5 and up -192085.500 -206126663 205742492 1.0000000
## 7.0 and up-1.5 and up 4129571.643 -50470200 58729343 1.0000000
## 7.1 and up-1.5 and up 32491247.833 -91938126 156920622 1.0000000
## 8.0 and up-1.5 and up -940401.167 -94487575 92606773 1.0000000
## NaN-1.5 and up -1186585.500 -150231090 147857919 1.0000000
## Varies with device-1.5 and up 38282276.906 -7107988 83672541 0.2825077
## 2.0 and up-1.6 and up 709660.748 -39419631 40838953 1.0000000
## 2.0.1 and up-1.6 and up 14038462.310 -64179980 92256905 1.0000000
## 2.1 and up-1.6 and up 1972222.589 -23559463 27503908 1.0000000
## 2.2 - 7.1.1-1.6 and up -400017.690 -202235984 201435949 1.0000000
## 2.2 and up-1.6 and up 5577.854 -22736014 22747169 1.0000000
## 2.3 and up-1.6 and up 2081402.455 -18259528 22422333 1.0000000
## 2.3.3 and up-1.6 and up 2181576.504 -20092469 24455622 1.0000000
## 3.0 and up-1.6 and up 1425034.436 -21444871 24294940 1.0000000
## 3.1 and up-1.6 and up 4703582.810 -61531930 70939095 1.0000000
## 3.2 and up-1.6 and up -169403.106 -38511527 38172721 1.0000000
## 4.0 and up-1.6 and up 4078143.949 -15405632 23561920 1.0000000
## 4.0.3 - 7.1.1-1.6 and up 7099882.310 -136228313 150428078 1.0000000
## 4.0.3 and up-1.6 and up 3268327.961 -16151740 22688396 1.0000000
## 4.1 - 7.1.1-1.6 and up 99599882.310 -102236084 301435849 0.9957732
## 4.1 and up-1.6 and up 5421470.770 -13723455 24566397 1.0000000
## 4.2 and up-1.6 and up 3265238.907 -18106707 24637185 1.0000000
## 4.3 and up-1.6 and up 2175881.048 -20866345 25218108 1.0000000
## 4.4 and up-1.6 and up 5642155.535 -14296800 25581111 1.0000000
## 4.4W and up-1.6 and up -397638.599 -63800834 63005557 1.0000000
## 5.0 - 6.0-1.6 and up -390117.690 -202226084 201445849 1.0000000
## 5.0 - 7.1.1-1.6 and up -400112.690 -202236079 201435854 1.0000000
## 5.0 - 8.0-1.6 and up 9599882.310 -133728313 152928078 1.0000000
## 5.0 and up-1.6 and up 2767472.824 -17898244 23433189 1.0000000
## 5.1 and up-1.6 and up -108219.508 -46842314 46625875 1.0000000
## 6.0 and up-1.6 and up 574815.477 -32533205 33682835 1.0000000
## 7.0 - 7.1.1-1.6 and up 599882.310 -201236084 202435849 1.0000000
## 7.0 and up-1.6 and up 4921539.453 -31270206 41113285 1.0000000
## 7.1 and up-1.6 and up 33283215.644 -84238597 150805028 1.0000000
## 8.0 and up-1.6 and up -148433.356 -84289869 83993002 1.0000000
## NaN-1.6 and up -394617.690 -143722813 142933578 1.0000000
## Varies with device-1.6 and up 39074244.716 19351580 58796910 0.0000000
## 2.0.1 and up-2.0 and up 13328801.562 -70528893 97186496 1.0000000
## 2.1 and up-2.0 and up 1262561.841 -38308325 40833449 1.0000000
## 2.2 - 7.1.1-2.0 and up -1109678.437 -205197271 202977914 1.0000000
## 2.2 and up-2.0 and up -704082.894 -38534866 37126700 1.0000000
## 2.3 and up-2.0 and up 1371741.707 -35066447 37809930 1.0000000
## 2.3.3 and up-2.0 and up 1471915.757 -36079666 39023497 1.0000000
## 3.0 and up-2.0 and up 715373.688 -37192683 38623430 1.0000000
## 3.1 and up-2.0 and up 3993922.062 -68814946 76802790 1.0000000
## 3.2 and up-2.0 and up -879063.854 -49706378 47948251 1.0000000
## 4.0 and up-2.0 and up 3368483.201 -32598247 39335213 1.0000000
## 4.0.3 - 7.1.1-2.0 and up 6390221.562 -140091722 152872165 1.0000000
## 4.0.3 and up-2.0 and up 2558667.213 -33373591 38490926 1.0000000
## 4.1 - 7.1.1-2.0 and up 98890221.562 -105197371 302977814 0.9968951
## 4.1 and up-2.0 and up 4711810.023 -31072493 40496113 1.0000000
## 4.2 and up-2.0 and up 2555578.159 -34468039 39579195 1.0000000
## 4.3 and up-2.0 and up 1466220.300 -36546045 39478486 1.0000000
## 4.4 and up-2.0 and up 4932494.787 -31282835 41147825 1.0000000
## 4.4W and up-2.0 and up -1107299.347 -71349404 69134806 1.0000000
## 5.0 - 6.0-2.0 and up -1099778.438 -205187371 202987814 1.0000000
## 5.0 - 7.1.1-2.0 and up -1109773.438 -205197366 202977819 1.0000000
## 5.0 - 8.0-2.0 and up 8890221.562 -137591722 155372165 1.0000000
## 5.0 and up-2.0 and up 2057812.076 -34562674 38678298 1.0000000
## 5.1 and up-2.0 and up -817880.256 -56478133 54842372 1.0000000
## 6.0 and up-2.0 and up -134845.271 -44969309 44699618 1.0000000
## 7.0 - 7.1.1-2.0 and up -109778.438 -204197371 203977814 1.0000000
## 7.0 and up-2.0 and up 4211878.705 -42945629 51369387 1.0000000
## 7.1 and up-2.0 and up 32573554.896 -88774558 153921668 1.0000000
## 8.0 and up-2.0 and up -858094.104 -90265976 88549788 1.0000000
## NaN-2.0 and up -1104278.437 -147586222 145377665 1.0000000
## Varies with device-2.0 and up 38364583.969 2267885 74461283 0.0209578
## 2.1 and up-2.0.1 and up -12066239.722 -89999671 65867192 1.0000000
## 2.2 - 7.1.1-2.0.1 and up -14438480.000 -229286124 200409164 1.0000000
## 2.2 and up-2.0.1 and up -14032884.456 -91097356 63031587 1.0000000
## 2.3 and up-2.0.1 and up -11957059.856 -88347545 64433426 1.0000000
## 2.3.3 and up-2.0.1 and up -11856885.806 -88784683 65070911 1.0000000
## 3.0 and up-2.0.1 and up -12613427.874 -89715862 64489007 1.0000000
## 3.1 and up-2.0.1 and up -9334879.500 -108374750 89704991 1.0000000
## 3.2 and up-2.0.1 and up -14207865.417 -97225161 68809430 1.0000000
## 4.0 and up-2.0.1 and up -9960318.361 -86127046 66206409 1.0000000
## 4.0.3 - 7.1.1-2.0.1 and up -6938580.000 -168074313 154197153 1.0000000
## 4.0.3 and up-2.0.1 and up -10770134.349 -86920590 65380321 1.0000000
## 4.1 - 7.1.1-2.0.1 and up 85561420.000 -129286224 300409064 0.9999305
## 4.1 and up-2.0.1 and up -8616991.540 -84697745 67463762 1.0000000
## 4.2 and up-2.0.1 and up -10773223.403 -87444684 65898237 1.0000000
## 4.3 and up-2.0.1 and up -11862581.262 -89016305 65291142 1.0000000
## 4.4 and up-2.0.1 and up -8396306.775 -84680740 67888127 1.0000000
## 4.4W and up-2.0.1 and up -14436100.909 -111604604 82732402 1.0000000
## 5.0 - 6.0-2.0.1 and up -14428580.000 -229276224 200419064 1.0000000
## 5.0 - 7.1.1-2.0.1 and up -14438575.000 -229286219 200409069 1.0000000
## 5.0 - 8.0-2.0.1 and up -4438580.000 -165574313 156697153 1.0000000
## 5.0 and up-2.0.1 and up -11270989.486 -87748598 65206619 1.0000000
## 5.1 and up-2.0.1 and up -14146681.818 -101358082 73064719 1.0000000
## 6.0 and up-2.0.1 and up -13463646.833 -94197121 67269827 1.0000000
## 7.0 - 7.1.1-2.0.1 and up -13438580.000 -228286224 201409064 1.0000000
## 7.0 and up-2.0.1 and up -9116922.857 -91163222 72929377 1.0000000
## 7.1 and up-2.0.1 and up 19244753.333 -119438805 157928311 1.0000000
## 8.0 and up-2.0.1 and up -14186895.667 -125997155 97623363 1.0000000
## NaN-2.0.1 and up -14433080.000 -175568813 146702653 1.0000000
## Varies with device-2.0.1 and up 25035782.406 -51192403 101263968 0.9999992
## 2.2 - 7.1.1-2.1 and up -2372240.278 -204097926 199353446 1.0000000
## 2.2 and up-2.1 and up -1966644.734 -23707735 19774446 1.0000000
## 2.3 and up-2.1 and up 109179.866 -19106659 19325019 1.0000000
## 2.3.3 and up-2.1 and up 209353.916 -21042190 21460898 1.0000000
## 3.0 and up-2.1 and up -547188.153 -22422462 21328086 1.0000000
## 3.1 and up-2.1 and up 2731360.222 -63167336 68630056 1.0000000
## 3.2 and up-2.1 and up -2141625.695 -39898923 35615672 1.0000000
## 4.0 and up-2.1 and up 2105921.361 -16200159 20412001 1.0000000
## 4.0.3 - 7.1.1-2.1 and up 5127659.722 -138045196 148300516 1.0000000
## 4.0.3 and up-2.1 and up 1296105.373 -16942153 19534364 1.0000000
## 4.1 - 7.1.1-2.1 and up 97627659.722 -104098026 299353346 0.9969588
## 4.1 and up-2.1 and up 3449248.182 -14495757 21394253 1.0000000
## 4.2 and up-2.1 and up 1293016.319 -19011050 21597083 1.0000000
## 4.3 and up-2.1 and up 203658.459 -21851709 22259026 1.0000000
## 4.4 and up-2.1 and up 3669932.947 -15119878 22459744 1.0000000
## 4.4W and up-2.1 and up -2369861.187 -65421112 60681389 1.0000000
## 5.0 - 6.0-2.1 and up -2362340.278 -204088026 199363346 1.0000000
## 5.0 - 7.1.1-2.1 and up -2372335.278 -204098021 199353351 1.0000000
## 5.0 - 8.0-2.1 and up 7627659.722 -135545196 150800516 1.0000000
## 5.0 and up-2.1 and up 795250.235 -18764066 20354567 1.0000000
## 5.1 and up-2.1 and up -2080442.096 -48335935 44175051 1.0000000
## 6.0 and up-2.1 and up -1397407.112 -33826345 31031531 1.0000000
## 7.0 - 7.1.1-2.1 and up -1372340.278 -203098026 200353346 1.0000000
## 7.0 and up-2.1 and up 2949316.865 -32622265 38520899 1.0000000
## 7.1 and up-2.1 and up 31310993.055 -86021319 148643305 1.0000000
## 8.0 and up-2.1 and up -2120655.945 -85997209 81755898 1.0000000
## NaN-2.1 and up -2366840.278 -145539696 140806016 1.0000000
## Varies with device-2.1 and up 37102022.128 18541889 55662155 0.0000000
## 2.2 and up-2.2 - 7.1.1 405595.544 -200985977 201797168 1.0000000
## 2.3 and up-2.2 - 7.1.1 2481420.144 -198653209 203616049 1.0000000
## 2.3.3 and up-2.2 - 7.1.1 2581594.194 -198757718 203920906 1.0000000
## 3.0 and up-2.2 - 7.1.1 1825052.126 -199581050 203231154 1.0000000
## 3.1 and up-2.2 - 7.1.1 5103600.500 -205677159 215884360 1.0000000
## 3.2 and up-2.2 - 7.1.1 230614.583 -203513107 203974336 1.0000000
## 4.0 and up-2.2 - 7.1.1 4478161.639 -196571591 205527914 1.0000000
## 4.0.3 - 7.1.1-2.2 - 7.1.1 7499900.000 -238638998 253638798 1.0000000
## 4.0.3 and up-2.2 - 7.1.1 3668345.651 -197375243 204711934 1.0000000
## 4.1 - 7.1.1-2.2 - 7.1.1 99999900.000 -184216818 384216618 0.9999958
## 4.1 and up-2.2 - 7.1.1 5821488.460 -195195709 206838686 1.0000000
## 4.2 and up-2.2 - 7.1.1 3665256.597 -197576254 204906767 1.0000000
## 4.3 and up-2.2 - 7.1.1 2575898.738 -198849844 204001641 1.0000000
## 4.4 and up-2.2 - 7.1.1 6042173.225 -195052201 207136548 1.0000000
## 4.4W and up-2.2 - 7.1.1 2379.091 -209905579 209910337 1.0000000
## 5.0 - 6.0-2.2 - 7.1.1 9900.000 -284206818 284226618 1.0000000
## 5.0 - 7.1.1-2.2 - 7.1.1 -95.000 -284216813 284216623 1.0000000
## 5.0 - 8.0-2.2 - 7.1.1 9999900.000 -236138998 256138798 1.0000000
## 5.0 and up-2.2 - 7.1.1 3167490.514 -198000244 204335225 1.0000000
## 5.1 and up-2.2 - 7.1.1 291798.182 -205196550 205780146 1.0000000
## 6.0 and up-2.2 - 7.1.1 974833.167 -201849047 203798714 1.0000000
## 7.0 - 7.1.1-2.2 - 7.1.1 999900.000 -283216818 285216618 1.0000000
## 7.0 and up-2.2 - 7.1.1 5321557.143 -198028456 208671570 1.0000000
## 7.1 and up-2.2 - 7.1.1 33683233.333 -198378745 265745212 1.0000000
## 8.0 and up-2.2 - 7.1.1 251584.333 -216822520 217325688 1.0000000
## NaN-2.2 - 7.1.1 5400.000 -246133498 246144298 1.0000000
## Varies with device-2.2 - 7.1.1 39474262.406 -161598782 240547306 1.0000000
## 2.3 and up-2.2 and up 2075824.601 -13239576 17391226 1.0000000
## 2.3.3 and up-2.2 and up 2175998.650 -15626843 19978840 1.0000000
## 3.0 and up-2.2 and up 1419456.582 -17123484 19962397 1.0000000
## 3.1 and up-2.2 and up 4698004.956 -60170718 69566728 1.0000000
## 3.2 and up-2.2 and up -174980.961 -36104447 35754486 1.0000000
## 4.0 and up-2.2 and up 4072566.095 -10084609 18229741 1.0000000
## 4.0.3 - 7.1.1-2.2 and up 7094304.456 -135607412 149796020 1.0000000
## 4.0.3 and up-2.2 and up 3262750.107 -10806618 17332118 1.0000000
## 4.1 - 7.1.1-2.2 and up 99594304.456 -101797268 300985877 0.9956192
## 4.1 and up-2.2 and up 5415892.916 -8271190 19102976 0.9999395
## 4.2 and up-2.2 and up 3259661.053 -13400715 19920037 1.0000000
## 4.3 and up-2.2 and up 2170303.194 -16584757 20925363 1.0000000
## 4.4 and up-2.2 and up 5636577.681 -9140771 20413926 0.9999729
## 4.4W and up-2.2 and up -403216.453 -62377189 61570756 1.0000000
## 5.0 - 6.0-2.2 and up -395695.544 -201787268 200995877 1.0000000
## 5.0 - 7.1.1-2.2 and up -405690.544 -201797263 200985882 1.0000000
## 5.0 - 8.0-2.2 and up 9594304.456 -133107412 152296020 1.0000000
## 5.0 and up-2.2 and up 2761894.970 -12982307 18506097 1.0000000
## 5.1 and up-2.2 and up -113797.362 -44889724 44662130 1.0000000
## 6.0 and up-2.2 and up 569237.623 -29711929 30850404 1.0000000
## 7.0 - 7.1.1-2.2 and up 594304.456 -200797268 201985877 1.0000000
## 7.0 and up-2.2 and up 4915961.599 -28709185 38541108 1.0000000
## 7.1 and up-2.2 and up 33277637.789 -83479308 150034584 1.0000000
## 8.0 and up-2.2 and up -154011.211 -83223797 82915774 1.0000000
## NaN-2.2 and up -400195.544 -143101912 142301520 1.0000000
## Varies with device-2.2 and up 39068666.862 24584483 53552850 0.0000000
## 2.3.3 and up-2.3 and up 100174.050 -14511966 14712314 1.0000000
## 3.0 and up-2.3 and up -656368.019 -16161661 14848925 1.0000000
## 3.1 and up-2.3 and up 2622180.356 -61444384 66688744 1.0000000
## 3.2 and up-2.3 and up -2250805.561 -36710928 32209317 1.0000000
## 4.0 and up-2.3 and up 1996741.494 -7852069 11845552 1.0000000
## 4.0.3 - 7.1.1-2.3 and up 5018479.856 -137320388 147357347 1.0000000
## 4.0.3 and up-2.3 and up 1186925.506 -8535244 10909095 1.0000000
## 4.1 - 7.1.1-2.3 and up 97518479.856 -103616149 298653109 0.9968627
## 4.1 and up-2.3 and up 3340068.316 -5820156 12500293 0.9999903
## 4.2 and up-2.3 and up 1183836.452 -12012436 14380109 1.0000000
## 4.3 and up-2.3 and up 94478.593 -15663876 15852833 1.0000000
## 4.4 and up-2.3 and up 3560753.080 -7160417 14281923 0.9999989
## 4.4W and up-2.3 and up -2479041.054 -63612884 58654802 1.0000000
## 5.0 - 6.0-2.3 and up -2471520.144 -203606149 198663109 1.0000000
## 5.0 - 7.1.1-2.3 and up -2481515.144 -203616144 198653114 1.0000000
## 5.0 - 8.0-2.3 and up 7518479.856 -134820388 149857347 1.0000000
## 5.0 and up-2.3 and up 686070.369 -11332805 12704946 1.0000000
## 5.1 and up-2.3 and up -2189621.963 -45795322 41416078 1.0000000
## 6.0 and up-2.3 and up -1506586.978 -30028903 27015729 1.0000000
## 7.0 - 7.1.1-2.3 and up -1481520.144 -202616149 199653109 1.0000000
## 7.0 and up-2.3 and up 2840136.998 -29210198 34890472 1.0000000
## 7.1 and up-2.3 and up 31201813.189 -85111376 147515002 1.0000000
## 8.0 and up-2.3 and up -2229835.811 -84674743 80215071 1.0000000
## NaN-2.3 and up -2476020.144 -144814888 139862847 1.0000000
## Varies with device-2.3 and up 36992842.262 26679500 47306185 0.0000000
## 3.0 and up-2.3.3 and up -756542.069 -18723005 17209921 1.0000000
## 3.1 and up-2.3.3 and up 2522006.306 -62184286 67228299 1.0000000
## 3.2 and up-2.3.3 and up -2350979.611 -37986351 33284392 1.0000000
## 4.0 and up-2.3.3 and up 1896567.445 -11496667 15289802 1.0000000
## 4.0.3 - 7.1.1-2.3.3 and up 4918305.806 -137709647 147546258 1.0000000
## 4.0.3 and up-2.3.3 and up 1086751.457 -12213634 14387137 1.0000000
## 4.1 - 7.1.1-2.3.3 and up 97418305.806 -103921006 298757618 0.9969708
## 4.1 and up-2.3.3 and up 3239894.266 -9655429 16135218 1.0000000
## 4.2 and up-2.3.3 and up 1083662.403 -14932619 17099944 1.0000000
## 4.3 and up-2.3.3 and up -5695.457 -18191002 18179612 1.0000000
## 4.4 and up-2.3.3 and up 3460579.031 -10586597 17507755 1.0000000
## 4.4W and up-2.3.3 and up -2579215.103 -64383150 59224720 1.0000000
## 5.0 - 6.0-2.3.3 and up -2571694.194 -203911006 198767618 1.0000000
## 5.0 - 7.1.1-2.3.3 and up -2581689.194 -203921001 198757623 1.0000000
## 5.0 - 8.0-2.3.3 and up 7418305.806 -135209647 150046258 1.0000000
## 5.0 and up-2.3.3 and up 585896.320 -14475081 15646873 1.0000000
## 5.1 and up-2.3.3 and up -2289796.012 -46830078 42250486 1.0000000
## 6.0 and up-2.3.3 and up -1606761.027 -31538386 28324864 1.0000000
## 7.0 - 7.1.1-2.3.3 and up -1581694.194 -202921006 199757618 1.0000000
## 7.0 and up-2.3.3 and up 2739962.949 -30570750 36050676 1.0000000
## 7.1 and up-2.3.3 and up 31101639.139 -85565141 147768419 1.0000000
## 8.0 and up-2.3.3 and up -2330009.861 -85273017 80612997 1.0000000
## NaN-2.3.3 and up -2576194.194 -145204147 140051758 1.0000000
## Varies with device-2.3.3 and up 36892668.212 23154230 50631107 0.0000000
## 3.1 and up-3.0 and up 3278548.374 -61635270 68192366 1.0000000
## 3.2 and up-3.0 and up -1594437.542 -37605258 34416383 1.0000000
## 4.0 and up-3.0 and up 2653109.513 -11709279 17015498 1.0000000
## 4.0.3 - 7.1.1-3.0 and up 5674847.874 -137047373 148397069 1.0000000
## 4.0.3 and up-3.0 and up 1843293.525 -12432551 16119138 1.0000000
## 4.1 - 7.1.1-3.0 and up 98174847.874 -103231254 299580950 0.9965625
## 4.1 and up-3.0 and up 3996436.334 -9902803 17895676 1.0000000
## 4.2 and up-3.0 and up 1840204.471 -14994900 18675309 1.0000000
## 4.3 and up-3.0 and up 750846.612 -18159597 19661290 1.0000000
## 4.4 and up-3.0 and up 4217121.099 -10756944 19191186 1.0000000
## 4.4W and up-3.0 and up -1822673.035 -63843846 60198500 1.0000000
## 5.0 - 6.0-3.0 and up -1815152.126 -203221254 199590950 1.0000000
## 5.0 - 7.1.1-3.0 and up -1825147.126 -203231249 199580955 1.0000000
## 5.0 - 8.0-3.0 and up 8174847.874 -134547373 150897069 1.0000000
## 5.0 and up-3.0 and up 1342438.388 -14586545 17271422 1.0000000
## 5.1 and up-3.0 and up -1533253.944 -46374488 43307980 1.0000000
## 6.0 and up-3.0 and up -850218.959 -31227870 29527432 1.0000000
## 7.0 - 7.1.1-3.0 and up -825152.126 -202231254 200580950 1.0000000
## 7.0 and up-3.0 and up 3496505.017 -30215557 37208567 1.0000000
## 7.1 and up-3.0 and up 31858181.208 -84923826 148640188 1.0000000
## 8.0 and up-3.0 and up -1573467.792 -84678473 81531537 1.0000000
## NaN-3.0 and up -1819652.126 -144541873 140902569 1.0000000
## Varies with device-3.0 and up 37649210.281 22964382 52334038 0.0000000
## 3.2 and up-3.1 and up -4872985.917 -76712318 66966347 1.0000000
## 4.0 and up-3.1 and up -625438.861 -64425037 63174159 1.0000000
## 4.0.3 - 7.1.1-3.1 and up 2396299.500 -153275608 158068207 1.0000000
## 4.0.3 and up-3.1 and up -1435254.849 -65215426 62344916 1.0000000
## 4.1 - 7.1.1-3.1 and up 94896299.500 -115884460 305677059 0.9991734
## 4.1 and up-3.1 and up 717887.960 -62979046 64414822 1.0000000
## 4.2 and up-3.1 and up -1438343.903 -65839674 62962986 1.0000000
## 4.3 and up-3.1 and up -2527701.762 -67502431 62447027 1.0000000
## 4.4 and up-3.1 and up 938572.725 -63001502 64878647 1.0000000
## 4.4W and up-3.1 and up -5101221.409 -92912020 82709577 1.0000000
## 5.0 - 6.0-3.1 and up -5093700.500 -215874460 205687059 1.0000000
## 5.0 - 7.1.1-3.1 and up -5103695.500 -215884455 205677064 1.0000000
## 5.0 - 8.0-3.1 and up 4896299.500 -150775608 160568207 1.0000000
## 5.0 and up-3.1 and up -1936109.986 -66106532 62234312 1.0000000
## 5.1 and up-3.1 and up -4811802.318 -81459351 71835747 1.0000000
## 6.0 and up-3.1 and up -4128767.333 -73316282 65058747 1.0000000
## 7.0 - 7.1.1-3.1 and up -4103700.500 -214884460 206677059 1.0000000
## 7.0 and up-3.1 and up 217956.643 -70497060 70932973 1.0000000
## 7.1 and up-3.1 and up 28579632.833 -103716050 160875315 1.0000000
## 8.0 and up-3.1 and up -4852016.167 -108633288 98929256 1.0000000
## NaN-3.1 and up -5098200.500 -160770108 150573707 1.0000000
## Varies with device-3.1 and up 34370661.906 -29502296 98243619 0.9837049
## 4.0 and up-3.2 and up 4247547.056 -29713668 38208762 1.0000000
## 4.0.3 - 7.1.1-3.2 and up 7269285.417 -138733174 153271745 1.0000000
## 4.0.3 and up-3.2 and up 3437731.068 -30486974 37362436 1.0000000
## 4.1 - 7.1.1-3.2 and up 99769285.417 -103974436 303513007 0.9962860
## 4.1 and up-3.2 and up 5590873.877 -28177081 39358829 1.0000000
## 4.2 and up-3.2 and up 3434642.013 -31643936 38513220 1.0000000
## 4.3 and up-3.2 and up 2345284.154 -33775219 38465788 1.0000000
## 4.4 and up-3.2 and up 5811558.642 -28412827 40035944 1.0000000
## 4.4W and up-3.2 and up -228235.492 -69464871 69008400 1.0000000
## 5.0 - 6.0-3.2 and up -220714.583 -203964436 203523007 1.0000000
## 5.0 - 7.1.1-3.2 and up -230709.583 -203974431 203513012 1.0000000
## 5.0 - 8.0-3.2 and up 9769285.417 -136233174 155771745 1.0000000
## 5.0 and up-3.2 and up 2936875.930 -31715951 37589703 1.0000000
## 5.1 and up-3.2 and up 61183.598 -54324680 54447047 1.0000000
## 6.0 and up-3.2 and up 744218.583 -42497978 43986415 1.0000000
## 7.0 - 7.1.1-3.2 and up 769285.417 -202974436 204513007 1.0000000
## 7.0 and up-3.2 and up 5090942.560 -40555405 50737290 1.0000000
## 7.1 and up-3.2 and up 33452618.750 -87316264 154221501 1.0000000
## 8.0 and up-3.2 and up 20969.750 -88599162 88641102 1.0000000
## NaN-3.2 and up -225214.583 -146227674 145777245 1.0000000
## Varies with device-3.2 and up 39243647.823 5144820 73342476 0.0053696
## 4.0.3 - 7.1.1-4.0 and up 3021738.361 -139197168 145240645 1.0000000
## 4.0.3 and up-4.0 and up -809815.988 -8580573 6960941 1.0000000
## 4.1 - 7.1.1-4.0 and up 95521738.361 -105528014 296571491 0.9977933
## 4.1 and up-4.0 and up 1343326.821 -5711728 8398381 1.0000000
## 4.2 and up-4.0 and up -812905.042 -12645305 11019495 1.0000000
## 4.3 and up-4.0 and up -1902262.901 -16537488 12732962 1.0000000
## 4.4 and up-4.0 and up 1564011.586 -7425292 10553315 1.0000000
## 4.4W and up-4.0 and up -4475782.548 -65329795 56378230 1.0000000
## 5.0 - 6.0-4.0 and up -4468261.639 -205518014 196581491 1.0000000
## 5.0 - 7.1.1-4.0 and up -4478256.639 -205528009 196571496 1.0000000
## 5.0 - 8.0-4.0 and up 5521738.361 -136697168 147740645 1.0000000
## 5.0 and up-4.0 and up -1310671.125 -11813883 9192541 1.0000000
## 5.1 and up-4.0 and up -4186363.457 -47398875 39026148 1.0000000
## 6.0 and up-4.0 and up -3503328.472 -31420825 24414168 1.0000000
## 7.0 - 7.1.1-4.0 and up -3478261.639 -204528014 197571491 1.0000000
## 7.0 and up-4.0 and up 843395.504 -30669904 32356695 1.0000000
## 7.1 and up-4.0 and up 29205071.694 -86961283 145371427 1.0000000
## 8.0 and up-4.0 and up -4226577.306 -86464201 78011047 1.0000000
## NaN-4.0 and up -4472761.639 -146691668 137746145 1.0000000
## Varies with device-4.0 and up 34996100.767 26497329 43494872 0.0000000
## 4.0.3 and up-4.0.3 - 7.1.1 -3831554.349 -146041747 138378638 1.0000000
## 4.1 - 7.1.1-4.0.3 - 7.1.1 92500000.000 -153638898 338638898 0.9999806
## 4.1 and up-4.0.3 - 7.1.1 -1678411.540 -143851292 140494469 1.0000000
## 4.2 and up-4.0.3 - 7.1.1 -3834643.403 -146324502 138655215 1.0000000
## 4.3 and up-4.0.3 - 7.1.1 -4924001.262 -147673936 137825934 1.0000000
## 4.4 and up-4.0.3 - 7.1.1 -1457726.775 -143739706 140824253 1.0000000
## 4.4W and up-4.0.3 - 7.1.1 -7497520.909 -161985595 146990553 1.0000000
## 5.0 - 6.0-4.0.3 - 7.1.1 -7490000.000 -253628898 238648898 1.0000000
## 5.0 - 7.1.1-4.0.3 - 7.1.1 -7499995.000 -253638893 238638903 1.0000000
## 5.0 - 8.0-4.0.3 - 7.1.1 2500000.000 -198471569 203471569 1.0000000
## 5.0 and up-4.0.3 - 7.1.1 -4332409.486 -146718053 138053234 1.0000000
## 5.1 and up-4.0.3 - 7.1.1 -7208101.818 -155635442 141219238 1.0000000
## 6.0 and up-4.0.3 - 7.1.1 -6525066.833 -151241136 138191003 1.0000000
## 7.0 - 7.1.1-4.0.3 - 7.1.1 -6500000.000 -252638898 239638898 1.0000000
## 7.0 and up-4.0.3 - 7.1.1 -2178342.857 -147630886 143274200 1.0000000
## 7.1 and up-4.0.3 - 7.1.1 26183333.333 -157277769 209644436 1.0000000
## 8.0 and up-4.0.3 - 7.1.1 -7248315.667 -171340914 156844283 1.0000000
## NaN-4.0.3 - 7.1.1 -7494500.000 -208466069 193477069 1.0000000
## Varies with device-4.0.3 - 7.1.1 31974362.406 -110277468 174226193 1.0000000
## 4.1 - 7.1.1-4.0.3 and up 96331554.349 -104712034 297375143 0.9974405
## 4.1 and up-4.0.3 and up 2153142.809 -4724016 9030302 0.9999998
## 4.2 and up-4.0.3 and up -3089.054 -11730289 11724111 1.0000000
## 4.3 and up-4.0.3 and up -1092446.913 -15642751 13457857 1.0000000
## 4.4 and up-4.0.3 and up 2373827.574 -6476545 11224201 1.0000000
## 4.4W and up-4.0.3 and up -3665966.560 -64499611 57167678 1.0000000
## 5.0 - 6.0-4.0.3 and up -3658445.651 -204702034 197385143 1.0000000
## 5.0 - 7.1.1-4.0.3 and up -3668440.651 -204712029 197375148 1.0000000
## 5.0 - 8.0-4.0.3 and up 6331554.349 -135878638 148541747 1.0000000
## 5.0 and up-4.0.3 and up -500855.137 -10885410 9883700 1.0000000
## 5.1 and up-4.0.3 and up -3376547.469 -46560372 39807277 1.0000000
## 6.0 and up-4.0.3 and up -2693512.484 -30566584 25179559 1.0000000
## 7.0 - 7.1.1-4.0.3 and up -2668445.651 -203712034 198375143 1.0000000
## 7.0 and up-4.0.3 and up 1653211.492 -29820739 33127162 1.0000000
## 7.1 and up-4.0.3 and up 30014887.682 -86140799 146170574 1.0000000
## 8.0 and up-4.0.3 and up -3416761.318 -85639315 78805792 1.0000000
## NaN-4.0.3 and up -3662945.651 -145873138 138547247 1.0000000
## Varies with device-4.0.3 and up 35805916.755 27454232 44157602 0.0000000
## 4.1 and up-4.1 - 7.1.1 -94178411.540 -295195609 106838786 0.9982794
## 4.2 and up-4.1 - 7.1.1 -96334643.403 -297576154 104906867 0.9974826
## 4.3 and up-4.1 - 7.1.1 -97424001.262 -298849744 104001741 0.9969900
## 4.4 and up-4.1 - 7.1.1 -93957726.775 -295052101 107136648 0.9983618
## 4.4W and up-4.1 - 7.1.1 -99997520.909 -309905479 109910437 0.9976871
## 5.0 - 6.0-4.1 - 7.1.1 -99990000.000 -384206718 184226718 0.9999958
## 5.0 - 7.1.1-4.1 - 7.1.1 -99999995.000 -384216713 184216723 0.9999958
## 5.0 - 8.0-4.1 - 7.1.1 -90000000.000 -336138898 156138898 0.9999896
## 5.0 and up-4.1 - 7.1.1 -96832409.486 -298000144 104335325 0.9972294
## 5.1 and up-4.1 - 7.1.1 -99708101.818 -305196450 105780246 0.9968200
## 6.0 and up-4.1 - 7.1.1 -99025066.833 -301848947 103798814 0.9964674
## 7.0 - 7.1.1-4.1 - 7.1.1 -99000000.000 -383216718 185216718 0.9999967
## 7.0 and up-4.1 - 7.1.1 -94678342.857 -298028356 108671670 0.9984625
## 7.1 and up-4.1 - 7.1.1 -66316666.667 -298378645 165745312 1.0000000
## 8.0 and up-4.1 - 7.1.1 -99748315.667 -316822420 117325788 0.9987903
## NaN-4.1 - 7.1.1 -99994500.000 -346133398 146144398 0.9998939
## Varies with device-4.1 - 7.1.1 -60525637.594 -261598682 140547406 0.9999999
## 4.2 and up-4.1 and up -2156231.863 -13421947 9109483 1.0000000
## 4.3 and up-4.1 and up -3245589.722 -17426579 10935400 1.0000000
## 4.4 and up-4.1 and up 220684.765 -8008424 8449793 1.0000000
## 4.4W and up-4.1 and up -5819109.369 -66565479 54927260 1.0000000
## 5.0 - 6.0-4.1 and up -5811588.460 -206828786 195205609 1.0000000
## 5.0 - 7.1.1-4.1 and up -5821583.460 -206838781 195195614 1.0000000
## 5.0 - 8.0-4.1 and up 4178411.540 -137994469 146351292 1.0000000
## 5.0 and up-4.1 and up -2653997.946 -12514429 7206433 1.0000000
## 5.1 and up-4.1 and up -5529690.278 -48590483 37531102 1.0000000
## 6.0 and up-4.1 and up -4846655.293 -32528730 22835419 1.0000000
## 7.0 - 7.1.1-4.1 and up -4821588.460 -205838786 196195609 1.0000000
## 7.0 and up-4.1 and up -499931.317 -31804862 30804999 1.0000000
## 7.1 and up-4.1 and up 27861744.873 -88248258 143971747 1.0000000
## 8.0 and up-4.1 and up -5569904.127 -87727907 76588099 1.0000000
## NaN-4.1 and up -5816088.460 -147988969 136356792 1.0000000
## Varies with device-4.1 and up 33652773.946 25962535 41343012 0.0000000
## 4.3 and up-4.2 and up -1089357.859 -18157819 15979103 1.0000000
## 4.4 and up-4.2 and up 2376916.628 -10190904 14944737 1.0000000
## 4.4W and up-4.2 and up -3662877.506 -65147456 57821701 1.0000000
## 5.0 - 6.0-4.2 and up -3655356.597 -204896867 197586154 1.0000000
## 5.0 - 7.1.1-4.2 and up -3665351.597 -204906862 197576159 1.0000000
## 5.0 - 8.0-4.2 and up 6334643.403 -136155215 148824502 1.0000000
## 5.0 and up-4.2 and up -497766.083 -14189369 13193837 1.0000000
## 5.1 and up-4.2 and up -3373458.415 -47469532 40722615 1.0000000
## 6.0 and up-4.2 and up -2690423.430 -31956943 26576096 1.0000000
## 7.0 - 7.1.1-4.2 and up -2665356.597 -203906867 198576154 1.0000000
## 7.0 and up-4.2 and up 1656300.546 -31058078 34370679 1.0000000
## 7.1 and up-4.2 and up 30017976.737 -86479940 146515893 1.0000000
## 8.0 and up-4.2 and up -3413672.263 -86118989 79291644 1.0000000
## NaN-4.2 and up -3659856.597 -146149715 138830002 1.0000000
## Varies with device-4.2 and up 35809005.809 23587236 48030776 0.0000000
## 4.4 and up-4.3 and up 3466274.487 -11769678 18702227 1.0000000
## 4.4W and up-4.3 and up -2573519.647 -64658441 59511402 1.0000000
## 5.0 - 6.0-4.3 and up -2565998.738 -203991741 198859744 1.0000000
## 5.0 - 7.1.1-4.3 and up -2575993.738 -204001736 198849749 1.0000000
## 5.0 - 8.0-4.3 and up 7424001.262 -135325934 150173936 1.0000000
## 5.0 and up-4.3 and up 591591.776 -15583825 16767009 1.0000000
## 5.1 and up-4.3 and up -2284100.556 -47213466 42645265 1.0000000
## 6.0 and up-4.3 and up -1601065.571 -32108659 28906528 1.0000000
## 7.0 - 7.1.1-4.3 and up -1575998.738 -203001741 199849744 1.0000000
## 7.0 and up-4.3 and up 2745658.405 -31083541 36574857 1.0000000
## 7.1 and up-4.3 and up 31107334.596 -85708541 147923210 1.0000000
## 8.0 and up-4.3 and up -2324314.404 -85476906 80828277 1.0000000
## NaN-4.3 and up -2570498.738 -145320434 140179436 1.0000000
## Varies with device-4.3 and up 36898363.669 21946582 51850146 0.0000000
## 4.4W and up-4.4 and up -6039794.134 -67041066 54961478 1.0000000
## 5.0 - 6.0-4.4 and up -6032273.225 -207126648 195062101 1.0000000
## 5.0 - 7.1.1-4.4 and up -6042268.225 -207136643 195052106 1.0000000
## 5.0 - 8.0-4.4 and up 3957726.775 -138324253 146239706 1.0000000
## 5.0 and up-4.4 and up -2874682.711 -14199959 8450594 1.0000000
## 5.1 and up-4.4 and up -5750375.043 -49170021 37669270 1.0000000
## 6.0 and up-4.4 and up -5067340.058 -33304391 23169711 1.0000000
## 7.0 - 7.1.1-4.4 and up -5042273.225 -206136648 196052101 1.0000000
## 7.0 and up-4.4 and up -720616.082 -32517353 31076121 1.0000000
## 7.1 and up-4.4 and up 27641060.108 -88602505 143884625 1.0000000
## 8.0 and up-4.4 and up -5790588.892 -88137242 76556064 1.0000000
## NaN-4.4 and up -6036773.225 -148318753 136245206 1.0000000
## Varies with device-4.4 and up 33432089.181 23936114 42928065 0.0000000
## 5.0 - 6.0-4.4W and up 7520.909 -209900437 209915479 1.0000000
## 5.0 - 7.1.1-4.4W and up -2474.091 -209910432 209905484 1.0000000
## 5.0 - 8.0-4.4W and up 9997520.909 -144490553 164485595 1.0000000
## 5.0 and up-4.4W and up 3165111.423 -58077562 64407785 1.0000000
## 5.1 and up-4.4W and up 289419.091 -73924251 74503089 1.0000000
## 6.0 and up-4.4W and up 972454.076 -65508628 67453536 1.0000000
## 7.0 - 7.1.1-4.4W and up 997520.909 -208910437 210905479 1.0000000
## 7.0 and up-4.4W and up 5319178.052 -62750167 73388523 1.0000000
## 7.1 and up-4.4W and up 33680854.242 -97219756 164581464 1.0000000
## 8.0 and up-4.4W and up 249205.242 -101747728 102246139 1.0000000
## NaN-4.4W and up 3020.909 -154485053 154491095 1.0000000
## Varies with device-4.4W and up 39471883.315 -21459035 100402801 0.8508697
## 5.0 - 7.1.1-5.0 - 6.0 -9995.000 -284226713 284206723 1.0000000
## 5.0 - 8.0-5.0 - 6.0 9990000.000 -236148898 256128898 1.0000000
## 5.0 and up-5.0 - 6.0 3157590.514 -198010144 204325325 1.0000000
## 5.1 and up-5.0 - 6.0 281898.182 -205206450 205770246 1.0000000
## 6.0 and up-5.0 - 6.0 964933.167 -201858947 203788814 1.0000000
## 7.0 - 7.1.1-5.0 - 6.0 990000.000 -283226718 285206718 1.0000000
## 7.0 and up-5.0 - 6.0 5311657.143 -198038356 208661670 1.0000000
## 7.1 and up-5.0 - 6.0 33673333.333 -198388645 265735312 1.0000000
## 8.0 and up-5.0 - 6.0 241684.333 -216832420 217315788 1.0000000
## NaN-5.0 - 6.0 -4500.000 -246143398 246134398 1.0000000
## Varies with device-5.0 - 6.0 39464362.406 -161608682 240537406 1.0000000
## 5.0 - 8.0-5.0 - 7.1.1 9999995.000 -236138903 256138893 1.0000000
## 5.0 and up-5.0 - 7.1.1 3167585.514 -198000149 204335320 1.0000000
## 5.1 and up-5.0 - 7.1.1 291893.182 -205196455 205780241 1.0000000
## 6.0 and up-5.0 - 7.1.1 974928.167 -201848952 203798809 1.0000000
## 7.0 - 7.1.1-5.0 - 7.1.1 999995.000 -283216723 285216713 1.0000000
## 7.0 and up-5.0 - 7.1.1 5321652.143 -198028361 208671665 1.0000000
## 7.1 and up-5.0 - 7.1.1 33683328.333 -198378650 265745307 1.0000000
## 8.0 and up-5.0 - 7.1.1 251679.333 -216822425 217325783 1.0000000
## NaN-5.0 - 7.1.1 5495.000 -246133403 246144393 1.0000000
## Varies with device-5.0 - 7.1.1 39474357.406 -161598687 240547401 1.0000000
## 5.0 and up-5.0 - 8.0 -6832409.486 -149218053 135553234 1.0000000
## 5.1 and up-5.0 - 8.0 -9708101.818 -158135442 138719238 1.0000000
## 6.0 and up-5.0 - 8.0 -9025066.833 -153741136 135691003 1.0000000
## 7.0 - 7.1.1-5.0 - 8.0 -9000000.000 -255138898 237138898 1.0000000
## 7.0 and up-5.0 - 8.0 -4678342.857 -150130886 140774200 1.0000000
## 7.1 and up-5.0 - 8.0 23683333.333 -159777769 207144436 1.0000000
## 8.0 and up-5.0 - 8.0 -9748315.667 -173840914 154344283 1.0000000
## NaN-5.0 - 8.0 -9994500.000 -210966069 190977069 1.0000000
## Varies with device-5.0 - 8.0 29474362.406 -112777468 171726193 1.0000000
## 5.1 and up-5.0 and up -2875692.332 -46633840 40882455 1.0000000
## 6.0 and up-5.0 and up -2192657.347 -30947499 26562184 1.0000000
## 7.0 - 7.1.1-5.0 and up -2167590.514 -203335325 199000144 1.0000000
## 7.0 and up-5.0 and up 2154066.629 -30103372 34411505 1.0000000
## 7.1 and up-5.0 and up 30515742.820 -85854685 146886170 1.0000000
## 8.0 and up-5.0 and up -2915906.180 -85441545 79609733 1.0000000
## NaN-5.0 and up -3162090.514 -145547734 139223553 1.0000000
## Varies with device-5.0 and up 36306771.892 25366780 47246764 0.0000000
## 6.0 and up-5.1 and up 683034.985 -50148497 51514567 1.0000000
## 7.0 - 7.1.1-5.1 and up 708101.818 -204780246 206196450 1.0000000
## 7.0 and up-5.1 and up 5029758.961 -47862075 57921593 1.0000000
## 7.1 and up-5.1 and up 33391435.152 -90298015 157080885 1.0000000
## 8.0 and up-5.1 and up -40213.848 -92600923 92520495 1.0000000
## NaN-5.1 and up -286398.182 -148713738 148140942 1.0000000
## Varies with device-5.1 and up 39182464.224 -4138283 82503212 0.1558725
## 7.0 - 7.1.1-6.0 and up 25066.833 -202798814 202848947 1.0000000
## 7.0 and up-6.0 and up 4346723.976 -37000724 45694172 1.0000000
## 7.1 and up-6.0 and up 32708400.167 -86502109 151918909 1.0000000
## 8.0 and up-6.0 and up -723248.833 -87207642 85761144 1.0000000
## NaN-6.0 and up -969433.167 -145685503 143746636 1.0000000
## Varies with device-6.0 and up 38499429.239 10414690 66584168 0.0000952
## 7.0 and up-7.0 - 7.1.1 4321657.143 -199028356 207671670 1.0000000
## 7.1 and up-7.0 - 7.1.1 32683333.333 -199378645 264745312 1.0000000
## 8.0 and up-7.0 - 7.1.1 -748315.667 -217822420 216325788 1.0000000
## NaN-7.0 - 7.1.1 -994500.000 -247133398 245144398 1.0000000
## Varies with device-7.0 - 7.1.1 38474362.406 -162598682 239547406 1.0000000
## 7.1 and up-7.0 and up 28361676.190 -91741808 148465161 1.0000000
## 8.0 and up-7.0 and up -5069972.810 -92781156 82641211 1.0000000
## NaN-7.0 and up -5316157.143 -150768700 140136386 1.0000000
## Varies with device-7.0 and up 34152705.263 2491151 65814259 0.0165970
## 8.0 and up-7.1 and up -33431649.000 -175540008 108676710 1.0000000
## NaN-7.1 and up -33677833.333 -217138936 149783269 1.0000000
## Varies with device-7.1 and up 5791029.073 -110415632 121997690 1.0000000
## NaN-8.0 and up -246184.333 -164338783 163846414 1.0000000
## Varies with device-8.0 and up 39222678.073 -43071871 121517227 0.9976678
## Varies with device-NaN 39468862.406 -102782968 181720693 1.0000000ANOVA test for Content Rating vs Installs
# Filter out rows where Installs is 0 or NA and where Content.Rating is NA
data_for_anova <- data_final %>%
filter(!is.na(Content.Rating), !is.na(Installs), Installs > 0)
# Re-run the ANOVA test
install_anova <- aov(log10(Installs) ~ Content.Rating, data = data_for_anova)
# Display the results
print("\nANOVA test results for Installs by Content Rating:")## [1] "\nANOVA test results for Installs by Content Rating:"print(summary(install_anova))## Df Sum Sq Mean Sq F value Pr(>F)
## Content.Rating 5 743 148.68 41.95 <2e-16 ***
## Residuals 9638 34160 3.54
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOVA analysis : Revealed significant differences in install counts based on content rating (F(5, 9638) = 41.95, p < 2e-16). This indicates that various content ratings have a substantial impact on the number of installs, highlighting the importance of content quality and type in attracting users.
Chi-square Test for Content Rating vs Last Updated
# 3.2 Statistical Tests
# Chi-square test for independence
contingency_table <- table(data_time_analysis$Content.Rating, data_time_analysis$update_quarter)
# Perform the Chi-square test
chi_test <- chisq.test(contingency_table)
print("\nChi-square test for independence between Content Rating and Update Quarter:")## [1] "\nChi-square test for independence between Content Rating and Update Quarter:"print(chi_test)##
## Pearson's Chi-squared test
##
## data: contingency_table
## X-squared = 88.112, df = 15, p-value = 2.229e-12The P value is small signifying that there is statistically significant relationship between Content Rating and Last Updated quarter
Implications These findings suggest that regular updates are important for sustaining app installs, and that different content ratings can influence user engagement. Strategies aimed at timely updates and optimizing content ratings could enhance app performance and user acquisition.
Correlation
Correlation for all variables in data_final
Lets convert all the categorical variables into factors and then convert into numerical dataframe for calucalting the correlation matrix
# Step 1: Create a copy of the original data without specific columns
columns_to_remove <- c("App", "Scaled_Reviews", "update_year", "update_month",
"update_quarter", "days_since_update", "week_of_year", "Last.Updated","day_of_week","month_of_year","season")
data_numeric_or_factor <- data_final %>%
select(-one_of(columns_to_remove))
# Step 2: Convert specified categorical columns to factors
data_factor <- data_numeric_or_factor
# Step 3: Identify categorical columns
categorical_columns <- sapply(data_numeric_or_factor, is.factor)
# Step 4: Convert each categorical variable to numeric
data_final_numeric <- data_numeric_or_factor # Copy of the data
data_final_numeric[categorical_columns] <- lapply(data_numeric_or_factor[categorical_columns],
function(x) as.numeric(as.factor(x)))
# Step 5: Calculate Pearson correlation
correlation_matrix <- cor(data_final_numeric,method = "pearson", use = "complete.obs")
print(correlation_matrix)## Category Rating Reviews Size Installs
## Category 1.00000000 -0.03748571 0.017299610 -0.12509260 0.031658924
## Rating -0.03748571 1.00000000 0.055012062 0.05624989 0.040068378
## Reviews 0.01729961 0.05501206 1.000000000 0.07552366 0.625164525
## Size -0.12509260 0.05624989 0.075523661 1.00000000 0.040740457
## Installs 0.03165892 0.04006838 0.625164525 0.04074046 1.000000000
## Price -0.01376932 -0.01953409 -0.007597749 -0.02157185 -0.009405171
## Content.Rating -0.09387557 0.02591249 0.055620981 0.18280324 0.049807143
## Android.Ver 0.09094536 0.05804513 0.106335063 0.07354916 0.158737503
## log_Installs 0.05879716 0.06610220 0.207743211 0.25750081 0.263707724
## Price Content.Rating Android.Ver log_Installs
## Category -0.013769321 -0.093875566 0.090945364 0.05879716
## Rating -0.019534090 0.025912489 0.058045132 0.06610220
## Reviews -0.007597749 0.055620981 0.106335063 0.20774321
## Size -0.021571845 0.182803242 0.073549158 0.25750081
## Installs -0.009405171 0.049807143 0.158737503 0.26370772
## Price 1.000000000 -0.014487940 -0.009672448 -0.05623643
## Content.Rating -0.014487940 1.000000000 -0.003608702 0.12136585
## Android.Ver -0.009672448 -0.003608702 1.000000000 0.23854322
## log_Installs -0.056236427 0.121365850 0.238543220 1.00000000# Caluclate the spearman
correlation_matrix1 <- cor(data_final_numeric, method = "spearman", use = "complete.obs")
print(correlation_matrix1)## Category Rating Reviews Size Installs
## Category 1.00000000 -0.023074576 0.05850162 -0.11449196 0.06612057
## Rating -0.02307458 1.000000000 0.20073076 0.07385874 0.11994456
## Reviews 0.05850162 0.200730765 1.00000000 0.33110583 0.96770658
## Size -0.11449196 0.073858737 0.33110583 1.00000000 0.31032364
## Installs 0.06612057 0.119944559 0.96770658 0.31032364 1.00000000
## Price 0.01311436 0.053828940 -0.15071272 -0.04391102 -0.23202906
## Content.Rating -0.10818522 0.006106387 0.16509252 0.19593634 0.13938983
## Android.Ver 0.09009285 0.079794210 0.19115306 0.24624117 0.19460722
## log_Installs 0.06612057 0.119944559 0.96770658 0.31032364 1.00000000
## Price Content.Rating Android.Ver log_Installs
## Category 0.01311436 -0.108185222 0.090092845 0.06612057
## Rating 0.05382894 0.006106387 0.079794210 0.11994456
## Reviews -0.15071272 0.165092522 0.191153061 0.96770658
## Size -0.04391102 0.195936335 0.246241166 0.31032364
## Installs -0.23202906 0.139389834 0.194607223 1.00000000
## Price 1.00000000 -0.037143541 -0.099022432 -0.23202906
## Content.Rating -0.03714354 1.000000000 -0.005692711 0.13938983
## Android.Ver -0.09902243 -0.005692711 1.000000000 0.19460722
## log_Installs -0.23202906 0.139389834 0.194607223 1.00000000# Step 6: Plot the correlation matrix
corrplot(correlation_matrix, method = "color", addCoef.col = "black")
As seen installs has the highest correlation with the reviews.
As we can see from the both pearson and spearman have relatively different correlation matrices and plots. We can refer to the categorical variables correlation from the spearman.
Correlation Reviews
reviews_correlation_factor <- correlation_matrix[, "Reviews", drop = FALSE]
reviews_correlation_factor1 <- correlation_matrix1[, "Reviews", drop = FALSE]
# Print the correlation matrix for Reviews from numeric factor data
print(reviews_correlation_factor)## Reviews
## Category 0.017299610
## Rating 0.055012062
## Reviews 1.000000000
## Size 0.075523661
## Installs 0.625164525
## Price -0.007597749
## Content.Rating 0.055620981
## Android.Ver 0.106335063
## log_Installs 0.207743211# Step 6: Create a correlation plot for Reviews in data_numeric_or_factor
corrplot(reviews_correlation_factor, method = "color", addCoef.col = "black",
title = "Correlation of Reviews with Other Variables (Factor Data)",
tl.col = "black", tl.srt = 45)
corrplot(reviews_correlation_factor1, method = "color", addCoef.col = "black",
title = "Correlation of Reviews with Other Variables (Factor Data)",
tl.col = "black", tl.srt = 45)
As seen reviews has the highest correlation(positive) with the installs and then in spearman correlation matrix it has high correlation(positive) with content rating and android version meaning
Correlation with Rating
rating_correlation_factor <- correlation_matrix[, "Rating", drop = FALSE]
rating_correlation_factor1 <- correlation_matrix1[, "Rating", drop = FALSE]
# Print the correlation matrix for Reviews from numeric factor data
print(rating_correlation_factor)## Rating
## Category -0.03748571
## Rating 1.00000000
## Reviews 0.05501206
## Size 0.05624989
## Installs 0.04006838
## Price -0.01953409
## Content.Rating 0.02591249
## Android.Ver 0.05804513
## log_Installs 0.06610220# Step 6: Create a correlation plot for Reviews in data_numeric_or_factor
corrplot(rating_correlation_factor, method = "color", addCoef.col = "black",
title = "Correlation of Reviews with Other Variables (Factor Data)",
tl.col = "black", tl.srt = 45)
corrplot(rating_correlation_factor1, method = "color", addCoef.col = "black",
title = "Correlation of Reviews with Other Variables (Factor Data)",
tl.col = "black", tl.srt = 45)
Rating is not much correlated with any of the variables, only slightly positively correlated with reviews and installs which was also demonstrated through visualisation previously.
Correlation with Price
# correlation for Price
price_correlation_factor1 <- correlation_matrix1[, "Price", drop = FALSE]
print("Spearman Correlation of Price with Other Variables:")## [1] "Spearman Correlation of Price with Other Variables:"print(price_correlation_factor1)## Price
## Category 0.01311436
## Rating 0.05382894
## Reviews -0.15071272
## Size -0.04391102
## Installs -0.23202906
## Price 1.00000000
## Content.Rating -0.03714354
## Android.Ver -0.09902243
## log_Installs -0.23202906# Plot for correlation with Price
corrplot(price_correlation_factor1, method = "color", addCoef.col = "black",
title = "Correlation of Price with Other Variables (Spearman)",
tl.col = "black", tl.srt = 45)
Price vs. Log_Installs: -0.06, suggesting a very weak negative relationship between price and the number of installs.
Correlation with Category
# Correlation for Category
# convert the category variable into a suitable format if necessary
category_correlation_factor1 <- correlation_matrix1[, "Category", drop = FALSE]
print("Spearman Correlation of Category with Other Variables:")## [1] "Spearman Correlation of Category with Other Variables:"print(category_correlation_factor1)## Category
## Category 1.00000000
## Rating -0.02307458
## Reviews 0.05850162
## Size -0.11449196
## Installs 0.06612057
## Price 0.01311436
## Content.Rating -0.10818522
## Android.Ver 0.09009285
## log_Installs 0.06612057# Plot for correlation with Category
corrplot(category_correlation_factor1, method = "color", addCoef.col = "black",
title = "Correlation of Category with Other Variables (Spearman)",
tl.col = "black", tl.srt = 45)
# Correlation for Android Version
# Make sure to convert the category variable into a suitable format if necessary
version_correlation_factor1 <- correlation_matrix1[, "Android.Ver", drop = FALSE]
print("Spearman Correlation of Category with Other Variables:")## [1] "Spearman Correlation of Category with Other Variables:"print(category_correlation_factor1)## Category
## Category 1.00000000
## Rating -0.02307458
## Reviews 0.05850162
## Size -0.11449196
## Installs 0.06612057
## Price 0.01311436
## Content.Rating -0.10818522
## Android.Ver 0.09009285
## log_Installs 0.06612057# Plot for correlation with Category
corrplot(version_correlation_factor1, method = "color", addCoef.col = "black",
title = "Correlation of Category with Other Variables (Spearman)",
tl.col = "black", tl.srt = 45)
Correlation between time analysis variables VS Installs
# Create a new data frame with relevant variables for correlation analysis
correlation_data <- data_time_analysis %>%
select(days_since_update, update_year, update_month) %>%
mutate(log_installs = log10(data_final$Installs))
# Calculate the correlation matrix
correlation_matrix <- cor(correlation_data, method = "spearman", use = "complete.obs")
# Print the correlation matrix
print("Spearman Correlation Matrix:")## [1] "Spearman Correlation Matrix:"corrplot(correlation_matrix, method = "color",
col = colorRampPalette(c("red", "white", "blue"))(200),
type = "upper",
tl.col = "black", tl.srt = 45,
addCoef.col = "black", # Add correlation coefficients
number.cex = 0.7, # Adjust size of numbers
title = "Correlation Matrix", # Title
mar = c(0, 0, 1, 0)) # Margins
Correlation Analysis: A moderate negative correlation :(ρ=−0.3317) was found between the number of days since the last update and the log-transformed installs. This indicates that as the time since the last update increases, the number of installs tends to decrease. The relationship is statistically significant (p < 2.2e-16), suggesting that timely updates may be crucial for maintaining user engagement.
##correlation between Installs Vs Size
# Calculate Pearson correlation and perform the test
cor_test <- cor.test(data_clean$Size, data_clean$Installs, method = "pearson")
# Output the correlation coefficient and p-value
cor_test##
## Pearson's product-moment correlation
##
## data: data_clean$Size and data_clean$Installs
## t = 4.0069, df = 9657, p-value = 6.198e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02081430 0.06063426
## sample estimates:
## cor
## 0.04074046According to the relational hypothesis testing: 1. Correlation Coefficient (cor):Pearson correlation coefficient is 0.0407. This indicates a very weak positive relationship between Size and Installs—meaning that as app size increases, installs slightly tend to increase as well, but the effect is minimal.
P-values: The p-value is 6.198e-05 (or 0.00006198), which is much smaller than the conventional significance level (e.g., 0.05). This low p-value means that we can reject the null hypothesis (that there is no correlation) and conclude that x and y are not independent.
Confidence Interval: The 95% confidence interval for the correlation coefficient is between 0.0208 and 0.0606. This range is quite narrow and close to zero, further confirming that while the relationship is significant, the strength of the correlation is very low.